General Decay of Solutions of a Weak Viscoelastic Equation

Abstract

In this paper we consider the following viscoelastic equationin a bounded domain, and establish a general decay result which depends on the behavior of α and g. This work generalizes and improves earlier results in the literature.

Asymptotic behavior for a weak viscoelastic wave equations with a dynamic boundary and time varying delay term

“…Now we give some estimates related to the convolution operator. By direct calculations, as in [18,19] we find…”

“…Very little attention has been paid to this type of boundary conditions. We mention a few particular results in the one dimensional without delay term for a linear damping (m = 1) and g = 0 see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]32]. From the mathematical point of view, these problems do not neglect acceleration terms on the boundary.…”

Well-Posedness and General Decay of Solutions for the Heat Equation with a Time Varying Delay Term

“…where G i (t), i = 1, 8, denote the terms on the right side of the above equality in order. G 1 (t), G 2 (t) and G 3 (t) can be estimated as in [17] as follows, for any δ > 0. By Young's and Cauchy-Schwartz, we obtain…”

General decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan–Taylor damping with nonlinear delay and acoustic boundary conditions

“…For the relaxation function k and potential σ , as in [15], we assume that (H2) k, σ : R + → R + are nonincreasing differentiable functions such that k is a C 2 function and σ is a C 1 function satisfying…”