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Open AccessArticle

Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory

1
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2
Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1609; https://doi.org/10.3390/sym12101609
Received: 3 September 2020 / Revised: 17 September 2020 / Accepted: 23 September 2020 / Published: 27 September 2020
We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,ω)Δϕ(t,ω)+ϕt(t,ω)=1Γ(1ρ)0t(tσ)ρ|ϕ(σ,ω)|qdσ+μ(ω),t>0, ωRN imposing the condition (ϕ(0,ω),ϕt(0,ω))=(ϕ0(ω),ϕ1(ω))inRN, where N1, q>1, 0<ρ<1, ϕiLloc1(RN), i=0,1, μLloc1(RN) and μ0. Namely, it is shown that, if ϕ0,ϕ10, μL1(RN) and RNμ(ω)dω>0, then for all q>1, the considered problem has no global weak solution. View Full-Text
Keywords: damped wave equation; inhomogeneous term; nonlinear memory; global weak solution; nonexistence result damped wave equation; inhomogeneous term; nonlinear memory; global weak solution; nonexistence result
MDPI and ACS Style

Jleli, M.; Samet, B.; Vetro, C. Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory. Symmetry 2020, 12, 1609. https://doi.org/10.3390/sym12101609

AMA Style

Jleli M, Samet B, Vetro C. Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory. Symmetry. 2020; 12(10):1609. https://doi.org/10.3390/sym12101609

Chicago/Turabian Style

Jleli, Mohamed; Samet, Bessem; Vetro, Calogero. 2020. "Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory" Symmetry 12, no. 10: 1609. https://doi.org/10.3390/sym12101609

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