Asymptotic behavior of solutions of hyperbolic inequalities

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.

Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

(x 1 , . . . , x n ) ∈ Rn and t > 0, k 1 > 0 and k 2 > 0 are constants. The nonlinear termf(u) = O(u1+θ) and θ is a positive integer. Equation (1) is a model in variational form for the neoHookean elastomer rod and describes the motion of a neoHookean elastomer rod with internal damping; for more detailed physical background, we refer to [1]. In [1], the authors have studied a general class of ...

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...

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping

Compactness and Asymptotic Behavior of Entropy Solutions without Locally Bounded Variation for Hyperbolic Conservation Laws

We discuss some recent developments and ideas in studying the compactness and asymptotic behavior of entropy solutions without locally bounded variation for nonlinear hyperbolic systems of conservation laws. Several classes of nonlinear hyperbolic systems with resonant or linear degeneracy are analyzed. The relation of the asymptotic problems to other topics such as scale-invariance, compactnes...