General boundary stabilization of memory-type thermoelasticity with second sound
The authors study the time-asymptotic behavior of solutions to an \(n\)-dimensional system of visco-thermoelasticity with second sound in a bounded domain. For the Dirichlet problem, the exponential decay of solutions was established in [\textit{R. Racke}, Q. Appl. Math. 61, No. 2, 315--328 (2003; Zbl 1030.74018)] provided that \(\text{rot}\,u=\text{rot}\,q=0\). As a consequence, the radially symmetric solution to the Dirichlet problem decays exponentially. In this paper, the authors consider the case that a viscoelastic dissipation of memory type is acting on a part of the boundary. Exploiting the boundary dissipation and using careful energy estimates to construct an appropriate Lyapunov functional, the authors prove a general uniform stability (including polynomial decay) of the solution energy under suitable conditions on the boundary and the kernels of general-type decay.
scientific article; zbMATH DE number 6113166