𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Generalized Rankine–Hugoniot Condition and Shock Solutions for Quasilinear Hyperbolic Systems

✍ Scribed by Xiao-Biao Lin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
304 KB
Volume
168
Category
Article
ISSN
0022-0396

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to professor jack k. hale on the occasion of his 70th birthday For a quasilinear hyperbolic system, we use the method of vanishing viscosity to construct shock solutions. The solution consists of two regular regions separated by a free boundary (shock). We use Melnikov's integral to obtain a system of differentialÂalgebraic equations that governs the motion of the shock. For Lax shocks in conservation laws, these equations are equivalent to the Rankine Hugoniot condition. For under compressive shocks in conservation laws, or shocks in non-conservation systems, the Melnikov-type integral obtained in this paper generalizes the Rankine Hugoniot condition. Under some generic conditions, we show that the initial value problem of shock solutions can be solved as a free boundary problem by the method of characteristics.

📜 SIMILAR VOLUMES

Global solutions with shock waves to the
Global solutions with shock waves to the generalized Riemann problem for a class of quasilinear hyperbolic systems of balance laws II
✍ Zhi-Qiang Shao 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 265 KB 👁 1 views

## Abstract This work is a continuation of our previous work. In the present paper, we study the existence and uniqueness of global piecewise __C__^1^ solutions with shock waves to the generalized Riemann problem for general quasilinear hyperbolic systems of conservation laws with linear damping in

Point-wise decay estimate for the global
Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems
✍ Yi Zhou 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

## Abstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (__Commun. Partial Differential Equations__ 1994; **19**:1263–1317