The existence of multi-dimensional shock fronts

The existence of multi-dimensional shock fronts / Andrew Majda.

The short-time existence of discontinuous shock front solutions of a system of conservation laws in several space variables is proved below under suitable hypotheses. These shock front solutions are nonlinear progressing wave solutions associated with the nonlinear wave fields. The results developed...

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Bibliographic Details
Main Author: Majda, Andrew, 1949-
Format: eBook
Language:English
Published: Providence, R.I. : American Mathematical Society, ©1983.
Series:Memoirs of the American Mathematical Society ; no. 281.
Subjects:
Shock waves.
Differential equations, Hyperbolic > Numerical solutions.
Conservation laws (Physics)
Differential equations, Hyperbolic > Numerical solutions
Shock waves
Online Access:Click for online access
Table of Contents:
  • Introduction
  • Structural conditions and shock front initial data : some preliminary facts
  • The map to a fixed domain, compatibility conditions, and an approximate solution
  • The iteration scheme
  • Convergence of the iteration scheme
  • The main linear estimate
  • Appendix. Nonlinear calculus inequalities on Sobolev spaces weighted with time.

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