Existence and blow-up of solutions for von Karman equations with time delay and variable exponents

Jum-Ran Kang

Applied Mathematics and Computation, 2020, vol. 371, issue C

Abstract: We study the von Karman equations with time delay and variable exponents:utt+Δ2u+a|ut|q(·)−2ut+b|ut(t−τ)|q(·)−2ut(t−τ)=δ[u,F(u)]+c|u|p(·)−2uwhere a, δ and c are positive constants, b is a real number, τ > 0 represents the time delay and the exponents p(·) and q(·) are given measurable functions. For the blow-up result of solutions for the wave equation, many authors have been investigated. But there are few works on blow-up of solutions for von Karman equations. We show the blow-up result of solutions with positive initial energy as well as non-positive initial energy for the von Karman equations with time delay and variable exponents.

Keywords: Blow-up; Von Karman equations; Delay; Variable exponents (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:371:y:2020:i:c:s0096300319309099

DOI: 10.1016/j.amc.2019.124917

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