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.
Lingua originale | English |
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pagine (da-a) | 1-12 |
Numero di pagine | 12 |
Rivista | Symmetry |
Volume | 12 |
Stato di pubblicazione | Published - 2020 |
All Science Journal Classification (ASJC) codes
- ???subjectarea.asjc.1700.1701???
- ???subjectarea.asjc.1600.1601???
- ???subjectarea.asjc.2600.2600???
- ???subjectarea.asjc.3100.3101???