Global Existence and Asymptotic Stability in Nonlinear Heat Conduction

Global Existence and Asymptotic Behavior in Nonlinear Thermoviscoelasticity

We study global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to the system of nonlinear thermoviscoelasticity. Various boundary conditions are considered. It is shown that for any initial data (u0 , v0 , %0) # L _W 1, _H 1 there is a unique global solution (u, v, %)=(deformation gradient, velocity, temperature) such that u # C([0, ], L ), v # C((0...

Asymptotic Stability and Global Existence in Thermoelasticity with Symmetry

First we prove an exponential decay result for solutions of the equations of linear, homogeneous, isotropic thermoelasticity in bounded regions in two or three space dimensions if the rotation of the displacement vanishes. As a consequence, we describe the decay in radially symmetrical situations, and in a cylinder in R3. Then we establish the global existence of solutions to the corresponding ...

Global Existence and Asymptotic Behavior for a Nonlinear Viscoelastic Problem

In this paper the nonlinear viscoelastic wave equation |ut|utt −∆u−∆utt + ∫ t 0 g(t− τ)∆u(τ)dτ − γ∆ut = b|u|p−2u is considered. Using the potential well method a global existence and an exponential decay result are proved. Moreover, for sufficiently large values of the initial data and for a suitable relation between p and the relaxation function g, we establish an unboundedness result.

Mildly dissipative nonlinear Timoshenko systems — global existence and exponential stability

Local and global asymptotic stability of nonlinear cascade interconnected systems

K e y w o r d s N o n l i n e a r systems, Cascade systems, Discrete-time systems~ Local asymptotic stability, Global asymptotic stability.