Large-time asymptotic behaviors for the classical thermoelastic system

Abstract

In this paper, we study the classical thermoelastic system with Fourier's law of heat conduction in the whole space ${\mathbb{R}}^n$ when $n=1,2,3$, particularly, asymptotic profiles for its elastic displacement as large-time. We discover optimal growth estimates of the elastic displacement when $n=1,2$, whose growth rates coincide with those for the free wave model, whereas when $n=3$ the optimal decay rate is related to the Gaussian kernel. Furthermore, under a new condition for weighted datum, the large-time optimal leading term is firstly introduced by the combination of diffusion-waves, the heat kernel and singular components. We also illustrate a second-order profile of solution by diffusion-waves with weighted $L^1$ datum as a by-product. These results imply that wave-structure large-time behaviors hold only for the one- and two-dimensional thermoelastic systems.

References in corpus (1)

• Optimal large-time estimates and singular limits for thermoelastic plate equations with the Fourier law

Cited by in corpus (1)

• Large time behavior for the hyperbolic-parabolic coupled system with the regularity-loss structure