Symmetric hyperbolic systems and shock waves
Satyanad Kichenassamy (LMR)
TL;DR
This paper discusses the application of symmetric hyperbolic systems theory to construct smooth solutions and analyze singularities like shock waves in nonlinear wave equations within Mathematical Physics.
Contribution
It presents key techniques for applying symmetric hyperbolic systems theory to study nonlinear wave equations and their singularities.
Findings
Provides methods for constructing smooth solutions.
Analyzes the formation of shock waves.
Connects theory to applications in Mathematical Physics.
Abstract
The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the theory in Mathematical Physics.
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Taxonomy
TopicsNavier-Stokes equation solutions · Stability and Controllability of Differential Equations · Nonlinear Waves and Solitons