Journal of innovative applied mathematics and computational sciences
Volume 2, Numéro 1, Pages 92-107
2022-06-30
On A Viscoelastic Plate Equation With A Polynomial Source Term And P(x,t)- Laplacian Operator In The Presence Of Delay Term
Authors : Merah Ahlem . Mesloub Fatiha .
Abstract
In this paper, the blow-up of solutions for the following Dirichlet-Neumann problem to initial nonlinear viscoelastic plate equation with a lower order perturbation of $\vec{p}(x,t)$-Laplacian operator in the presence of time delay is obtained $$u_{tt}+\Delta ^{2}u +\Delta _{\vec{p}(x,t)}u-\int_{0}^{t}g(t-s)\Delta ^{2}u\left( s\right) ds-\mu _{1}\Delta u_{t}-\mu _{2}\Delta u_{t}(t-\tau )=u\left\vert u\right\vert ^{q-2}. $$ Under suitable conditions on $g$ and the variable exponent of the $\vec{p}(x,t)-$ Laplacian operator, we prove that any weak solution with nonpositive initial energy as well as positive initial energy blows up in a finite time.
Keywords
Blow-up, time delay, viscoelasticity, plate equation, nonstandard growth conditions, anisotropy
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