Reissig M., Schulze B.-W. (editors) New Trends in the Theory of Hyperbolic Equations

Springer, 2009. - 150 pages. This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over...

Oxford University Press, USA 2006. - 536 pages. Hyperbolic Partial Differential Equations(PDEs), and in particular first-order systems of conservation laws, have been a fashionable topic for over half a century. Many book shave been written, but few of them deal with genuinely multidimensional hyperbolic problems: in this respect the most classical, though not so well-known, references are the books by Reiko Sakamoto, by Jacques Chazarain and Al...

This volume is a collection of refereed original research papers and expository articles and stems from the scientific program of the 1997-98 Nonlinear PDE Emphasis Year at Northwestern University, which was jointly sponsored by Northwestern University and the National Science Foundation. Most of the papers presented are from the distinguished mathematicians who spoke at the International Conference on Nonlinear Partial Differential Equations, Ma...

Birkh?user Basel, 2009. - 352 pages. This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis. The book aims at spreading the seminal ideas...

American Mathematical Society, 1998. - 662 pages. This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: 1) representation formulas for solutions, 2) theory for linear partial differential equations, and 3) theory for nonlinear partial differential equations. Included are complete tr...

Second Edition. Springer, 2007. - 356 pages. This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and c...

2002. - 80 с. Представленная на английском языке работа - курс лекций Паламодова, подробно объясняющая решение уравнений математической физики из 8 частей. Contents Chapter 1: Differential equations of Mathematical Physics Differential equations of elliptic type Diffusion equations Wave equations Systems Nonlinear equations Hamilton-Jacobi theory Relativistic field theory Classification Initial and boundary value problems Inverse problems C...

Dover Publications Inc. , 1992. - 245 pages. Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text.

CRC Press, 2010. - 282 pages. Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field. After linking continuum mechanics and quasilinear partial differential equations, the book discusses the scalar conservation l...

Springer, 1999. - 563 pages. This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic probl...