Abstract
This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies g′(t)≤−ξ(t)G(g(t)), we establish an explicit general decay rates without imposing a restrictive growth assumption on the damping term. This general condition allows us to recover the exponential and polynomial rates. Our results improve and extend some existing results in the literature. We preform some numerical experiments to illustrate our theoretical results.
Highlights
Denote Ω to be an open bounded domain of R2 having a smooth boundary ∂Ω
Let n stands for the unit outer normal to ∂Ω
Since J20 (t) = J 0 (λ2 t) + λ2 tJ 00 (λ2 t), applying the strict convexity of J on (0, s2 ], we find that J20 (t), J2 (t) > 0 on
Summary
Denote Ω to be an open bounded domain of R2 having a smooth boundary ∂Ω. Let n stands for the unit outer normal to ∂Ω. In the case of one-dimensional, Gorka [11] used some compactness results to obtain the global existence of weak solutions to the initial-boundary value problem of Equation (4). Al-Gharabli and Messaoudi [12] proved the global existence and the exponential decay of solutions of the following plate equation: utt + ∆ u + u + h(ut ) = ku ln |u|,. In 2008, Messaoudi [25,26] generalized the decay rates permitting an extended class of relaxation functions. He considered a relaxation function that satisfy.
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