Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities

Salim A. Messaoudi; Ala A. Talahmeh

doi:10.3934/dcdss.2021107

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2022, Volume 15, Issue 5: 1233-1245. Doi: 10.3934/dcdss.2021107

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Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities

Salim A. Messaoudi^1, and
Ala A. Talahmeh^2,

1.
Department of Mathematics, University of Sharjah, P.O. Box 27272, Sharjah, UAE
2.
Department of Mathematics, Birzeit University, West Bank, Palestine

Received: June 30, 2021

Revised: July 31, 2021

Early access: September 2021

Published: May 2022

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Abstract

This work is concerned with a system of wave equations with variable-exponent nonlinearities acting in both equations. We, first, discuss the well-posedness then prove a blow up result for solutions with negative initial energy.

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Mathematics Subject Classification: 35D30, 35B40, 35B44, 35L70.

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