Long-time Behavior for a Nonlinear Plate Equation with Thermal Memory

Details Long-time Behavior for a Nonlinear Plate Equation with Thermal Memory Long-time Behavior for a Nonlinear Plate Equation with Thermal Memory

2008-04-10

arxiv.org/abs/0804.1806v2

J. Math. Anal. Appl., Vol.348 (2008), 650-670

Mathematics

Analysis of PDEs

32 pages

Scientific paper

We consider a nonlinear plate equation with thermal memory effects due to non-Fourier heat flux laws. First we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we use a suitable Lojasiewicz--Simon type inequality to show the convergence of global solutions to single steady states as time goes to infinity under the assumption that the nonlinear term $f$ is real analytic. Moreover, we provide an estimate on the convergence rate.

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