Abstract
This paper is concerned with the existence of traveling waves for the scalar hyperbolic-parabolic balance law. Using a phase-plane analysis method, we first prove the existence of an increasing traveling wave solution in $C^{1}(\mathbb{R})$ . Then we construct a family of discontinuous periodic traveling wave entropy solutions.
Highlights
We consider the discontinuous traveling waves for the scalar hyperbolic-parabolic balance law ∂u ∂ ∂ + f (u) = ∂u a(u)+ g(u), x ∈ R, t >, ( . ) ∂t ∂x ∂x∂x where a ∈ C (R) with a(s) ≥ for s ∈ R
Considering the scalar hyperbolic-parabolic balance law ( . ), namely the case n = of ( . ), we present the basic assumption on the viscosity term supp a = [ak, bk], k=
2 Preliminaries and main results we present some closely related results and definitions of entropy solutions
Summary
1 Introduction We consider the discontinuous traveling waves for the scalar hyperbolic-parabolic balance law When a(u) ≡ ε, Wu and Xing [ ] considered the traveling waves of the following scalar viscous balance law: In Section , we prove the existence of discontinuous traveling waves. Sinestrari [ ] studied the discontinuous traveling waves of the scalar hyperbolic balance law
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