Download or read book Nonlinear Problems in Mathematical Physics and Related Topics written by Michael Sh. Birman and published by Springer Science & Business Media. This book was released on 2002 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics in this volume reflect the fields of mathematics in which Professor O.A. Ladyzhenskaya obtained her most influential results. One of the main topics considered is the set of Navier-Stokes equations and their solutions.
Download or read book Nonlinear Problems in Mathematical Physics and Related Topics I written by Michael Sh. Birman and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday. O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva. Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role. Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary. Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.
Download or read book Nonlinear Problems in Mathematical Physics and Related Topics II written by Michael Sh. Birman and published by Springer. This book was released on 2014-01-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics reflect the fields of mathematics in which Professor O.A. Ladyzhenskaya obtained her most influential results. One of the main topics considered in the volume is the Navier-Stokes equations. This subject is investigated in many different directions. In particular, the existence and uniqueness results are obtained for the Navier-Stokes equations in spaces of low regularity. A sufficient condition for the regularity of solutions to the evolution Navier-Stokes equations in the three-dimensional case is derived and the stabilization of a solution to the Navier-Stokes equations to the steady-state solution and the realization of stabilization by a feedback boundary control are discussed in detail. Connections between the regularity problem for the Navier-Stokes equations and a backward uniqueness problem for the heat operator are also clarified. Generalizations and modified Navier-Stokes equations modeling various physical phenomena such as the mixture of fluids and isotropic turbulence are also considered. Numerical results for the Navier-Stokes equations, as well as for the porous medium equation and the heat equation, obtained by the diffusion velocity method are illustrated by computer graphs. Some other models describing various processes in continuum mechanics are studied from the mathematical point of view. In particular, a structure theorem for divergence-free vector fields in the plane for a problem arising in a micromagnetics model is proved. The absolute continuity of the spectrum of the elasticity operator appearing in a problem for an isotropic periodic elastic medium with constant shear modulus (the Hill body) is established. Time-discretization problems for generalized Newtonian fluids are discussed, the unique solvability of the initial-value problem for the inelastic homogeneous Boltzmann equation for hard spheres, with a diffusive term representing a random background acceleration is proved and some qualitative properties of the solution are studied. An approach to mathematical statements based on the Maxwell model and illustrated by the Lavrent'ev problem on the wave formation caused by explosion welding is presented. The global existence and uniqueness of a solution to the initial boundary-value problem for the equations arising in the modelling of the tension-driven Marangoni convection and the existence of a minimal global attractor are established. The existence results, regularity properties, and pointwise estimates for solutions to the Cauchy problem for linear and nonlinear Kolmogorov-type operators arising in diffusion theory, probability, and finance, are proved. The existence of minimizers for the energy functional in the Skyrme model for the low-energy interaction of pions which describes elementary particles as spatially localized solutions of nonlinear partial differential equations is also proved. Several papers are devoted to the study of nonlinear elliptic and parabolic operators. Versions of the mean value theorems and Harnack inequalities are studied for the heat equation, and connections with the so-called growth theorems for more general second-order elliptic and parabolic equations in the divergence or nondivergence form are investigated. Additionally, qualitative properties of viscosity solutions of fully nonlinear partial differential inequalities of elliptic and degenerate elliptic type are clarified. Some uniqueness results for identification of quasilinear elliptic and parabolic equations are presented and the existence of smooth solutions of a class of Hessian equations on a compact Riemannian manifold without imposing any curvature restrictions on the manifold is established.
Download or read book Nonlinear Problems in Mathematical Physics and Related Topics II written by Michael Sh. Birman and published by Springer. This book was released on 2012-09-21 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics reflect the fields of mathematics in which Professor O.A. Ladyzhenskaya obtained her most influential results. One of the main topics considered in the volume is the Navier-Stokes equations. This subject is investigated in many different directions. In particular, the existence and uniqueness results are obtained for the Navier-Stokes equations in spaces of low regularity. A sufficient condition for the regularity of solutions to the evolution Navier-Stokes equations in the three-dimensional case is derived and the stabilization of a solution to the Navier-Stokes equations to the steady-state solution and the realization of stabilization by a feedback boundary control are discussed in detail. Connections between the regularity problem for the Navier-Stokes equations and a backward uniqueness problem for the heat operator are also clarified. Generalizations and modified Navier-Stokes equations modeling various physical phenomena such as the mixture of fluids and isotropic turbulence are also considered. Numerical results for the Navier-Stokes equations, as well as for the porous medium equation and the heat equation, obtained by the diffusion velocity method are illustrated by computer graphs. Some other models describing various processes in continuum mechanics are studied from the mathematical point of view. In particular, a structure theorem for divergence-free vector fields in the plane for a problem arising in a micromagnetics model is proved. The absolute continuity of the spectrum of the elasticity operator appearing in a problem for an isotropic periodic elastic medium with constant shear modulus (the Hill body) is established. Time-discretization problems for generalized Newtonian fluids are discussed, the unique solvability of the initial-value problem for the inelastic homogeneous Boltzmann equation for hard spheres, with a diffusive term representing a random background acceleration is proved and some qualitative properties of the solution are studied. An approach to mathematical statements based on the Maxwell model and illustrated by the Lavrent'ev problem on the wave formation caused by explosion welding is presented. The global existence and uniqueness of a solution to the initial boundary-value problem for the equations arising in the modelling of the tension-driven Marangoni convection and the existence of a minimal global attractor are established. The existence results, regularity properties, and pointwise estimates for solutions to the Cauchy problem for linear and nonlinear Kolmogorov-type operators arising in diffusion theory, probability, and finance, are proved. The existence of minimizers for the energy functional in the Skyrme model for the low-energy interaction of pions which describes elementary particles as spatially localized solutions of nonlinear partial differential equations is also proved. Several papers are devoted to the study of nonlinear elliptic and parabolic operators. Versions of the mean value theorems and Harnack inequalities are studied for the heat equation, and connections with the so-called growth theorems for more general second-order elliptic and parabolic equations in the divergence or nondivergence form are investigated. Additionally, qualitative properties of viscosity solutions of fully nonlinear partial differential inequalities of elliptic and degenerate elliptic type are clarified. Some uniqueness results for identification of quasilinear elliptic and parabolic equations are presented and the existence of smooth solutions of a class of Hessian equations on a compact Riemannian manifold without imposing any curvature restrictions on the manifold is established.
Download or read book Nonlinear Problems in Mathematical Physics and Related Topics written by Michael Sh Birman and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Problems in Mathematical Physics and Related Topics I written by Michael Sh. Birman and published by Springer. This book was released on 2012-10-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday. O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva. Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role. Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary. Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.
Download or read book Recent Topics in Nonlinear PDE II written by K. Masuda and published by Elsevier. This book was released on 1986-09-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of lectures delivered at the second meeting on the subject of nonlinear partial differential equations, held at Tohoku University, 27-29 February 1984. The topics presented at the conference range over various fields of mathematical physics.
Download or read book Nonlinear Dynamics written by H.G Solari and published by Routledge. This book was released on 2019-01-22 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work
Download or read book Mathematical Topics In Nonlinear Kinetic Theory Ii written by Nicola Bellomo and published by World Scientific Publishing Company. This book was released on 1991-04-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the relevant mathematical aspects related to the kinetic equations for moderately dense gases with particular attention to the Enskog equation.
Download or read book Nonlinear Problems in Mathematical Physics and Related Topics I written by Michael Sh. Birman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday. O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva. Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role. Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary. Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.
Download or read book Trends in Partial Differential Equations of Mathematical Physics written by José F. Rodrigues and published by Springer Science & Business Media. This book was released on 2005-01-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable results on exact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, Stokes and Navier-Stokes systems, his methods and contributions to the inverstigation of free boundary problems, in particular in fluid mechanics, are well known to specialists all over the world. The International Conference on "Trends in Partial Differential Equations of Mathematical Physics" was held on the occasion of his 70th birthday in ??bidos (Portugal) from June 7 to 10, 2003. The conference consisted of thirty-eight invited and contributed lectures and gathered, in the charming and unique medieval town of ??bidos, about sixty participants from fifteen countries. This book contains twenty original contributions on many topics related to V.A. Solonnikov's work, selected from the invited talks of the conference.
Download or read book Group Theoretical Methods for Integration of Nonlinear Dynamical Systems written by A.N. Leznov and published by Springer Science & Business Media. This book was released on 1992-04-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.
Download or read book Recent Topics in Nonlinear PDE III written by K. Masuda and published by Elsevier. This book was released on 2011-09-22 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems treated in this volume concern nonlinear partial differential equations occurring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. Presented are new results and new methods for analysis in bifurcation, singular perturbation, variational methods, stability analysis, rearrangement, energy inequalities, etc.
Download or read book Mathematical Topics In Nonlinear Kinetic Theory written by Nicola Bellomo and published by World Scientific. This book was released on 1989-01-01 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has the aim of dealing with the Nonlinear evolution problems related to the spatially dependent Boltzmann and Enskog equations.
Download or read book Dispersive Nonlinear Problems in Mathematical Physics written by Piero D'Ancona and published by . This book was released on 2005 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Topics in Nonlinear PDE IV written by Masayasu Mimura and published by Elsevier. This book was released on 1989 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
Download or read book Nonlinear Analysis Theory and Methods written by Nikolaos S. Papageorgiou and published by Springer. This book was released on 2019-02-26 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
