On a viscoelastic plate equation with a polynomial source term and p (x,t)-Laplacian operator in the presence of delay term

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Ahlem Merah
Fatiha Mesloub


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 p⃗ (x,t)p→(x,t)-Laplacian operator in the presence of time delay is obtained

utt+Δ2u+Δp⃗ (x,t)u−∫t0g(t−s)Δ2u(s)ds−μ1Δut−μ2Δut(t−τ)=u|u|q−2.utt+Δ2u+Δp→(x,t)u−∫0tg(t−s)Δ2u(s)ds−μ1Δut−μ2Δut(t−τ)=u|u|q−2.

Under suitable conditions on gg and the variable exponent of the p⃗ (x,t)−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.




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Merah, A. and Mesloub, F. 2022. On a viscoelastic plate equation with a polynomial source term and p (x,t)-Laplacian operator in the presence of delay term. Journal of Innovative Applied Mathematics and Computational Sciences. 2, 1 (Jun. 2022), 92–107.
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