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Solution Blow-Up for a Fractional Fourth-Order Equation of Moore–Gibson–Thompson Type with Nonlinearity Nonlocal in Time

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Abstract

We reformulate the fourth-order equation of the Moore–Gibson–Thompson (MGT) type to a fractional semilinear fourth-order equation with structural damping and a time-nonlocal nonlinearity. The solution blow-up for this problem is established by the test function method. First, we recall some definitions and elementary properties of the fractional derivatives, and then we study the absence of global weak solutions.

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Acknowledgments

The authors are grateful to the anonymous referees for careful reading and important observations and suggestions for improving the present paper.

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Authors and Affiliations

  1. Larbi Tebessi University, Tebessa, 12002, Algeria

    F. Mesloub & A. Merah

  2. College of Sciences and Arts, Qassim University, Ar Rass, 51921, Saudi Arabia

    S. Boulaaras

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  1. F. Mesloub
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  2. A. Merah
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  3. S. Boulaaras
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Correspondence to F. Mesloub.

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Mesloub, F., Merah, A. & Boulaaras, S. Solution Blow-Up for a Fractional Fourth-Order Equation of Moore–Gibson–Thompson Type with Nonlinearity Nonlocal in Time. Math Notes 113, 72–79 (2023). https://doi.org/10.1134/S000143462301008X

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  • DOI: https://doi.org/10.1134/S000143462301008X

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