Download or read book Methods for the Temporal Approximation of Nonlinear Nonautonomous Evolution Equations written by Monika Eisenmann and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Evolution Equations written by Songmu Zheng and published by CRC Press. This book was released on 2004-07-08 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator
Download or read book Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics written by Victor G. Zvyagin and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.
Download or read book Approximation of Nonlinear Evolution Systems written by Jerome and published by Academic Press. This book was released on 1983-04-22 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation of Nonlinear Evolution Systems
Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke and published by Birkhäuser. This book was released on 2015-08-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
Download or read book Evolution Equations And Approximations written by Kazufumi Ito and published by World Scientific. This book was released on 2002-05-24 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and the Lie-Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory.In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier-Stokes equation and scalar conservation equation are given.
Download or read book Solution Methods for Certain Evolution Equations written by José Manuel Vega-Guzmán and published by . This book was released on 2013 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.
Download or read book Nonlinear Evolution Equations and Potential Theory written by J. Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Download or read book Nonlinear Evolution Equations and Dynamical Systems written by Sandra Carillo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.
Download or read book Nonlinear Evolution Equations written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-05 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Evolution Equation presents state-of-the-art theories and results on nonlinear evolution equation, showing related mathematical methods and applications. The basic concepts and research methods of infinite dimensional dynamical systems are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and students in applied mathematics and physics.
Download or read book Nonlinear Evolution Equations And Their Applications Proceedings Of The Luso chinese Symposium written by Tatsien Li and published by World Scientific. This book was released on 1999-08-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.
Download or read book Method of Rothe in Evolution Equations written by Jozef Kačur and published by . This book was released on 1985 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compactness Methods for Nonlinear Evolutions written by Ioan I. Vrabie and published by Longman Scientific and Technical. This book was released on 1987 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exact and Approximate Analytical Methods for Solving Nonlinear Evolution Equations written by Muna Said Al-Ghabshiyah and published by . This book was released on 2017 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Evolution Equations written by Antonio Degasperis and published by . This book was released on 1990 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer Science & Business Media. This book was released on 2010-09-17 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke and published by Vieweg+Teubner Verlag. This book was released on 2014-04-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an elementary, self contained introduction into some important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The presentation is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data.
