Discontinuity, Nonlinearity, and Complexity
Wellposedness and Stability for a MooreGibsonThompson Equation with Internal Distributed Delay
Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 693703  DOI:10.5890/DNC.2021.12.009
Abdelkader Braik$^1$, Abderrahmane Beniani$^2$, Khaled Zennir$^3$
$^1$ Department of Sciences and Technology, University of Hassiba Ben Bouali, Chlef, Algeria
$^2$ Department of Mathematics, BP 284, University Centre BELHADJ Bouchaib Ain Tmouchent 46000, Algeri
$^3$ Department of Mathematics, College of Sciences
and Arts, Qassim University, ArRass, Saudi Arabia
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Abstract
In this work, we consider the MooreGibsonThompson equation with distributed delay.
We prove, under an appropriate assumptions and a smallness conditions on the parameters $\alpha $, $\beta$, $\gamma$ and $\mu$, that this problem is wellposed and then by introducing suitable energy and Lyapunov functionals, the solution of \eqref{p1} and \eqref{p2} decays to zero as $t$ tends to infinity.
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