Existence and decay of solution to coupled system of viscoelastic wave equations with strong damping in Rn

Abstract

In this paper, we establish a general decay rate properties of solutions for a coupled system of viscoelastic wave equations in IRn under some assumptions on g1; g2 and linear forcing terms. We exploit a density function to introduce weighted spaces for solutions and using an appropriate perturbed energy method. The questions of global existence in the nonlinear cases is also proved in Sobolev spaces using the well known Galerkin method.

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

“…They proved the global nonexistence of solutions with positive initial energy when the kernel of the memories satisfies some appropriate conditions. For more information about the results on the system of viscoelastic equations with constant exponents, we refer to the selected papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Related to the system of Kirchhoff-type equations, Li et al [21] considered the following system of viscoelastic wave equations of Kirchhoff-type with strong damping terms:…”

“…They proved the global nonexistence of solutions with positive initial energy when the kernel of the memories satisfies some appropriate conditions. For more information about the results on the system of viscoelastic equations with constant exponents, we refer to the selected papers [5–20].…”