We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory φtt (t, ω) − ∆φ(t, ω) + φt (t, ω) =1 ∫t Γ(1−ρ) 0(t − σ)−ρ |φ(σ, ω)|q dσ + µ(ω), t > 0, ω ∈ RN imposing the condition (φ(0, ω), φt (0, ω)) = (φ0 (ω), φ1 (ω)) in RN, where N ≥ 1, q > 1, 0 < ρ < 1, φi ∈ L1loc(RN), i = 0, 1, µ ∈ L1loc(RN) and µ ̸≡ 0. Namely, it is shown that, if φ0, φ1 ≥ 0, ∫ µ ∈ L1 (RN) and µ(ω) dω > 0, then for all q > 1, the considered problem has no global RNweak solution.
Jleli M., Samet B., & Vetro C. (2020). Large time behavior for inhomogeneous damped wave equations with nonlinear memory. SYMMETRY, 12(10), 1-12.
Data di pubblicazione: | 2020 |
Titolo: | Large time behavior for inhomogeneous damped wave equations with nonlinear memory |
Autori: | VETRO, Calogero (Corresponding) |
Citazione: | Jleli M., Samet B., & Vetro C. (2020). Large time behavior for inhomogeneous damped wave equations with nonlinear memory. SYMMETRY, 12(10), 1-12. |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3390/sym12101609 |
Abstract: | We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory φtt (t, ω) − ∆φ(t, ω) + φt (t, ω) =1 ∫t Γ(1−ρ) 0(t − σ)−ρ |φ(σ, ω)|q dσ + µ(ω), t > 0, ω ∈ RN imposing the condition (φ(0, ω), φt (0, ω)) = (φ0 (ω), φ1 (ω)) in RN, where N ≥ 1, q > 1, 0 < ρ < 1, φi ∈ L1loc(RN), i = 0, 1, µ ∈ L1loc(RN) and µ ̸≡ 0. Namely, it is shown that, if φ0, φ1 ≥ 0, ∫ µ ∈ L1 (RN) and µ(ω) dω > 0, then for all q > 1, the considered problem has no global RNweak solution. |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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