F. Mesloub, A. Merah, S. Boulaaras, “Solution Blow-Up for a Fractional Fourth-Order Equation of Moore–Gibson–Thompson Type with Nonlinearity Nonlocal in Time”, Mat. Zametki, 2023, Volume 113, Issue 1,Pages <nobr>72

This article is cited in 2 papers

Papers published in the English version of the journal

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

F. Mesloub^a, A. Merah^a, S. Boulaaras^b

^a Laboratory of Mathematics, Informatics, and Systems, Larbi Tebessi University, Tebessa, 12002 Algeria
^b Department of Mathematics, College of Sciences and Arts, Qassim University, Ar Rass, 51921 Saudi Arabia

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.

Keywords: prime number, arithmetic progression, fractional part, Bombieri–Vinogradov theorem, exponential sum.

Received: 03.02.2022
Revised: 18.05.2022

Language: English