Nonlinear wave equations perturbed by viscous terms

著者

書誌事項

Nonlinear wave equations perturbed by viscous terms

Viktor P. Maslov, Petr P. Mosolov ; translated from the Russian by M.A. Shishkova

（De Gruyter expositions in mathematics, v. 31）

Walter de Gruyter, 2000

タイトル別名

Uravnenii︠a︡ odnomernogo barotropnogo gaza.

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注記

"Russian original ed : Uravnenii︠a︡ odnomernogo barotropnogo gaza. Publisher: Nauka, Moscow 1990" -- T.p. verso

Includes bibliographical references (p. [239]-243) and index

内容説明・目次

内容説明

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Aix-Marseille Universite, France Katrin Wendland, Trinity College Dublin, Dublin, Ireland Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

目次

  • The Cauchy problem for an infinite one-dimensional system of particles with nonlinear viscoelastic ties
  • main estimates for the solution of the discrete problem
  • interpolation of grid functions
  • existence, uniqueness, and smoothness theorems for the solution of the Cauchy problem for a partial differential equation that is the limit equation for a nonlinear viscoelastic system
  • estimates for differences between solutions of the Cauchy problem for the basic equation (4.17)
  • the Cauchy problem for an equation in general form
  • the Cauchy problem for a second-order hyperbolic equation with small third-order viscous terms
  • solvability of the Cauchy problem
  • solvability of the Cauchy problem for a system of equations
  • solution behavior in the case of vanishing viscosity
  • acoustic approximation
  • asymptotics of a shock wave in a barotropic medium.

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