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November/December 2014 On a viscoelastic plate equation with strong damping and $\overrightarrow{p}(x,t)-$ Laplacian. Existence and uniqueness
S. Antontsev, J. Ferreira
Differential Integral Equations 27(11/12): 1147-1170 (November/December 2014).

Abstract

In this paper, we study the class of non-linear viscoelastic equation with lower order perturbation of $\overrightarrow{p}(x,t)-$ Laplacian type and a memory term \[ u_{tt}+\Delta^{2}u-\Delta_{\overrightarrow{p}(x,t)}u+\int_{0}^{t}g(t-s)\Delta u(s)ds -\epsilon\Delta u_{t}+f(u) =0\text{, } \] \[ (x,t)\in Q_{T}=\Omega\times(0,T),\quad\Omega\in\mathbb{R}^{n}. \] We prove local and global existence and uniqueness of weak solutions. These results are obtained assuming a strong damping $\epsilon\Delta u_{t}$ $(\epsilon>0)$ acting in the domain and provided the memory term decays exponentially and $f(u)$ is a nonlinear perturbation.

Citation

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S. Antontsev. J. Ferreira. "On a viscoelastic plate equation with strong damping and $\overrightarrow{p}(x,t)-$ Laplacian. Existence and uniqueness." Differential Integral Equations 27 (11/12) 1147 - 1170, November/December 2014.

Information

Published: November/December 2014
First available in Project Euclid: 18 August 2014

zbMATH: 1340.35342
MathSciNet: MR3250757

Subjects:
Primary: 335L70, 35B40, 35L45

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 11/12 • November/December 2014
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