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Solvability Of The Moore–Gibson–Thompson Equation With Viscoelastic Memory Term And Integral Condition Via Galerkin Method

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  • SALAH BOULAARAS

    (Department of Mathematics, College of Sciences and Arts, Ar-Rass, Qassim University, Kingdom of Saudi Arabia2Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Algeria)

Abstract

We consider the following abstract version of the Moore–Gibson–Thompson (MGT) equation: auttt + βutt + c2Δu + bΔu t +∫0th(t − s)Δu(s)ds = 0, depending on the parameters a, β, b > 0, and h is a convex and nonnegative memory kernel. The related energy has been shown to decay exponentially by Boulaaras et al., Math. Meth. Appl. Sci. 42 (2019) 2664–2679; Lasiecka et al., Z. Angew. Math. Phys. 67 (2016) 17. Here, in this original work, the solvability of the abstract version of nonlocal mixed boundary value problem for the MGT equation via Galerkin’s method is discussed.

Suggested Citation

  • Salah Boulaaras, 2021. "Solvability Of The Moore–Gibson–Thompson Equation With Viscoelastic Memory Term And Integral Condition Via Galerkin Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-18, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21400211
    DOI: 10.1142/S0218348X21400211
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