Exponential decay for solutions of coupled nonlinear viscoelastic and heat system
Abstract
Following the paper of Ben Aissa\cite{akram} dealing with internal stability of coupled non-degenrate Kirchhoff system via heat conduction, this manuscript concerns with the problem of the following nonlinear viscoelastic equation
$$|y_t|^ly_{tt}-\gamma \Delta y_{tt}-\Delta y +\alpha \Delta \theta=0$$ coupled to linear heat equation in a bounded domain. So under a clever adaptation of the well-known Fadeo-Galerkin approximation method, we establish existence and uniqueness of solution to this coupled system. Meanwhile, using the piecewise multiplied method, we show the exponenetial decay of the solution
Published
2023-11-26
Section
Articles