Abstract
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(1−ρ)∫0t(t−σ)−ρ|ϕ(σ,ω)|qdσ+μ(ω),t>0, ω∈RN imposing the condition (ϕ(0,ω),ϕt(0,ω))=(ϕ0(ω),ϕ1(ω))inRN, where N≥1, q>1, 0<ρ<1, ϕi∈Lloc1(RN), i=0,1, μ∈Lloc1(RN) and μ≢0. Namely, it is shown that, if ϕ0,ϕ1≥0, μ∈L1(RN) and ∫RNμ(ω)dω>0, then for all q>1, the considered problem has no global weak solution.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献