Download or read book Existence of Solutions for Generalized Cauchy Goursat Type Problems for Hyperbolic Equations written by Eduardo A. Luna and published by . This book was released on 1973 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Goursat Problem for a Hyperbolic System written by Robert P.. Holten and published by . This book was released on 1958 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Cauchy Problem written by Sigeru Mizohata and published by Academic Press. This book was released on 2014-05-10 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.
Download or read book Generalized Goursat Problem for a Hyperbolic System written by Robert Peter Holten and published by . This book was released on 1958 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Hyperbolic Equations Spectral Theory and Wavelet Transformations written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2003-10-24 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on recent developments in non-linear and hyperbolic equations. In the first contribution, the singularities of the solutions of several classes of non-linear partial differential equations are investigated. Applications concern the Monge-Ampère equation, quasi-linear systems arising in fluid mechanics as well as integro-differential equations for media with memory. There follows an article on L_p-L_q decay estimates for Klein-Gordon equations with time-dependent coefficients, explaining, in particular, the influence of the relation between the mass term and the wave propagation speed. The next paper addresses questions of local existence of solutions, blow-up criteria, and C^8 regularity for quasilinear weakly hyperbolic equations. Spectral theory of semibounded selfadjoint operators is the topic of a further contribution, providing upper and lower bounds for the bottom eigenvalue as well as an upper bound for the second eigenvalue in terms of capacitary estimates. TOC:Contributions: Nonlinear PDE. Singularities, Propagation, Applications (P.R. Popivanov).- From Wave to Klein-Gordon Type Decay Rates (F. Hirosawa and M. Reissig).- Local Solutions to Quasilinear Qeakly Hyperbolic Differential Equations (M. Dreher).- S(M,g)-pseudo-differential Calculus of Manifolds (F. Baldus).- Domain Perturbations and Capacity in General Hilbert Spaces and Applications to Spectral Theory (A. Noll).- An Interpolation Family between Gabor and Wavelet Transformations (B. Nazaret and M. Holschneider).- Formes de Torsion Analytique et Fibrations Singulières (Xiaonan Ma).- Regularisation of Secondary Characteristic Classes and Unusual Index Formulas for Operator-Valued Symbols (G. Rozenblum).
Download or read book Kernel Determination Problems in Hyperbolic Integro Differential Equations written by Durdimurod K. Durdiev and published by Springer Nature. This book was released on 2023-06-18 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional “impacts” or “explosions”. This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.
Download or read book New Trends in the Theory of Hyperbolic Equations written by Michael Reissig and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.
Download or read book Hyperbolic Equations and Related Topics written by Sigeru Mizohata and published by Academic Press. This book was released on 2014-05-10 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic Equations and Related Topics covers the proceedings of the Taniguchi International Symposium, held in Katata, Japan on August 27-31, 1984 and in Kyoto, Japan on September 3-5, 1984. The book focuses on the mathematical analyses involved in hyperbolic equations. The selection first elaborates on complex vector fields; holomorphic extension of CR functions and related problems; second microlocalization and propagation of singularities for semi-linear hyperbolic equations; and scattering matrix for two convex obstacles. Discussions focus on the construction of asymptotic solutions, singular vector fields and Leibniz formula, second microlocalization along a Lagrangean submanifold, and hypo-analytic structures. The text then ponders on the Cauchy problem for effectively hyperbolic equations and for uniformly diagonalizable hyperbolic systems in Gevrey classes. The book takes a look at generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem and analytic and Gevrey well-posedness of the Cauchy problem for second order weakly hyperbolic equations with coefficients irregular in time. The selection is a dependable reference for researchers interested in hyperbolic equations.
Download or read book Hyperbolic Equations and General Relativity written by Marica Minucci and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is divided into three parts. In the first part, the hyperbolic equations' theory is analysed, the second part concerns the Cauchy problem in General Relativity, whereas the third part gives a modern perspective of General Relativity.In the first part, the study of systems of partial differential equations allows the introduction of the concept of wave-like propagation and the definition of hyperbolic equation is given. Thus, once the definition of Riemann kernel is given, Riemann's method to solve a hyperbolic equation in two variables is shown. The discussion moves on the fundamental solutions and its relation to Riemann kernel is pointed out. Therefore, the study of the fundamental solutions concludes by showing how to build them providing some examples of solution with odd and even number of variables. Moreover, the fundamental solution of the scalar wave equation with smooth initial conditions is studied.In the second part, following the work of Fourès-Bruhat, the problem of finding a solution to the Cauchy problem for Einstein field equations in vacuum with non-analytic initial data is presented by first studying under which assumptions second-order systems of partial differential equations, linear and hyperbolic, with n functions and four variables admit a solution. Hence, it is shown how to turn non-linear systems of partial differential equations into linear systems of the same type for which the previous results hold. These considerations allow us to prove the existence and uniqueness of the solution to the Cauchy problem for Einstein's vacuum field equations with non-analytic initial data. Eventually, the causal structure of space-time is studied. The definitions of strong causality, stable causality and global hyperbolicity are given and the relation between the property of global hyperbolicity and the existence of Cauchy surfaces is stressed. In the third part, Riemann's method is used to study the news function describing the gravitational radiation produced in axisymmetric black hole collisions at the speed of light. More precisely, since the perturbative field equations may be reduced to equations in two independent variables, as was proved by D'Eath and Payne, the Green function can be analysed by studying the corresponding second-order hyperbolic operator with variable coefficients. Thus, an integral representation of the solution in terms of the Riemann kernel function can be given.
Download or read book Long Time Existence of Solutions to Cauchy and Mixed Problems for Second Order Quasilinear Hyperbolic Equations written by Paul Godin and published by . This book was released on 1989 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cauchy s Problem for Hyperbolic Equations written by Lars Gårding and published by . This book was released on 1958 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Problems written by Song Jiang and published by World Scientific. This book was released on 2012 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."
Download or read book Hyperbolic Problems and Regularity Questions written by Mariarosaria Padula and published by Springer Science & Business Media. This book was released on 2007-01-21 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
Download or read book The Cauchy Goursat Problem written by P. DuChateau and published by . This book was released on 1972 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract theorems of existence, uniqueness and regularity of the solution are proved for a differential equation whose solution takes its values in a sequence of Banach spaces called a Banach scale. The abstract theorems are then applied to obtain existence, uniqueness and regularity theorems of a classical nature bearing on that generalization of the Cauchy problem of partial differential equations known as the Goursat problem. All the results so obtained remain true in the case when the equations involve more general operators than partial differential operators, (e.g. pseudo-differential operators).
Download or read book On Some Generalized Cauchy Problems and the Convexity of Their Solutions written by Robert W. Carroll and published by . This book was released on 1959 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper treats a class of generalized Cauchy problems for equations of the type of the Euler-Poisson-Darboux (EPD) equation. In the case of the EPD equation Weinstein's [46] results about the convexity and growth of the solution are extended to the most general multiply subharmonic initial data and some of his criteria are sharpened. The conditions under which there will be a convexity theorem for equations of this type are examined. For the EPD equation of index n-1 a study is made of when the generalized solution is a solution in the usual sense.
Download or read book Generalized Functions and Partial Differential Equations written by Avner Friedman and published by Courier Corporation. This book was released on 2005-12-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.
Download or read book Global Classical Solutions for Quasilinear Hyperbolic Systems written by Daqian Li and published by . This book was released on 1994-09-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic presentation of the global classical solution and the global classical discontinuous solution to quasilinear hyperbolic systems. This book is a result of the author's research on the Cauchy problem, boundary value problems, free boundary problems and the generalised Riemann problem.
