Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping

Nonlinear Hyperbolic Surface Waves

We describe examples of hyperbolic surface waves and discuss their connection with initial boundary value and discontinuity problems for hyperbolic systems of PDEs that are weakly but not uniformly stable.

Convergence Rates to Nonlinear Di®usion Waves for Weak Entropy Solutions to p-System with Damping

In this paper, we study the asymptotic behavior of weak entropy solutions to the Cauchy problem of the so-called p-system with damping. The convergence rates to nonlinear di®usion waves are obtained. The analysis is based on the viscosity method and energy method.

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a …xed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W s;p p > 1; s < 1 + 1 p of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This impl...

Reaction-diffusion waves with nonlinear boundary conditions

A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method. 1. Formulation of the problem. Reaction-diffusion problems with nonlinear boundary conditions arise in various applications. In physiology, such problems describe in particular development of atheroscle...

Construction and Qualitative Behavior of Solutions for a System of Nonlinear Hyperbolic Conservation Laws with Damping