Some problems on planar rarefaction waves for hyperbolic conservation laws

關於雙曲守恒律方程稀疏波的一些問題研究

Student thesis: Doctoral Thesis

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Author(s)

  • Jing CHEN

Related Research Unit(s)

Detail(s)

Awarding Institution
Supervisors/Advisors
Award date2 Oct 2009

Abstract

In this thesis, we study the stability of planar rarefaction waves to the Cauchy and the initial boundary value problems for hyperbolic conservation laws. Precisely, we study the following problems: In Chapter 2, we aim to prove the convergence rates of solutions to strong rarefaction waves for two-dimensional viscous conservation law with boundary. In Chapter 3, we study the decay rates of strong planar rarefaction waves to scalar conservation laws with degenerate viscosity. In Chapter 4, we investigate the asymptotic stability of the weak rarefaction wave for Cauchy problem for generalized KdV-Burgers-Kuramoto equation. The analysis is based on a priori estimates and the standard L2-energy method.

    Research areas

  • Cauchy problem, Wave equation, Differential equations, Hyperbolic, Conservation laws (Mathematics)