Well‐Posedness and Blow‐Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Nebi Yılmaz, Erhan Pişkin and Ercan Çelik

Advances in Mathematical Physics, 2023, vol. 2023, issue 1

Abstract: In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo–Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p(⋅) and q(⋅). Finally, we prove a finite‐time blow‐up result for negative initial energy.

Date: 2023
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https://doi.org/10.1155/2023/8866861

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:8866861

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