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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 1
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Research Article

Blow-up phenomenon for a semilinear pseudo-parabolic equation involving variable source

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Pages 88-103 | Received 10 Jul 2020, Accepted 16 Jun 2021, Published online: 01 Jul 2021
 

Abstract

We consider a semilinear pseudo-parabolic equation with nonlinearities of variable exponent subject to Dirichlet boundary conditions utΔutΔu=up(x).We prove that the nonnegative classical solutions blow-up in finite time with arbitrary positive initial energy and suitable large initial values. Also, employing a differential inequality technique, we obtain an upper bound for blow-up time if p(.) and the initial value satisfies some conditions.

2010 Mathematics Subject Classifications:

Acknowledgments

The author would like to thank the anonymous referee(s) and the handling editor(s) for fruitful comments through the significant improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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