Global existence and asymptotic behavior of classical solutions to Goursat problem for diagonalizable quasilinear hyperbolic system

Asymptotic behavior of global classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small BV data

In this paper, we investigate the asymptotic behavior of global classical solutions to the mixed initial-boundary value problem with small BV data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space {(t, x)|t ≥ 0, x ≥ 0}. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the...

Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation

The initial boundary value problem for a class of hyperbolic equation with nonlinear dissipative term u tt − n i1 ∂/∂x i |∂u/∂x i | p−2 ∂u/∂x i a|u t | q−2 u t b|u| r−2 u in a bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in W 1,p 0 ΩΩ and show the asymptotic behavior of the global solutions through the use of an important l...

Large Solutions of Quasilinear Elliptic System of Competitive Type: Existence and Asymptotic Behavior

On Asymptotic Behavior of Global Solutions for Hyperbolic Hemivariational Inequalities

In this paper we study the existence of global weak solutions for a hyperbolic differential inclusion with a discontinuous and nonlinear multivalued term. Also we investigate the asymptotic behavior of solutions.

Global Existence of Solutions to a Hyperbolic-parabolic System

In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get L2-estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.