Blow up and global existence in a nonlinear viscoelastic wave equation

By Salim A. Messaoudi. 2003

248 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/03c6dba96ffcb645e911a97fd8a398114630a1e8

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global existence and uniform stability of solutions for a quasilinear viscoelastic problem (2007, unknown): “Messaoudi S.A., Blow up and global existence in a nonlinear viscoelastic wave equation, Mathematische Nachrichten Vol. 260 (2003), 58-66.”
Blow‐up of solutions for a viscoelastic wave equation with variable exponents (2019, background): “He showed a blow-up result of solutions for (6) with negative initial energy and p > m.”
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping. (2004, unknown): “Messaoudi [17] considered the equation utt −∆u + ∫ t 0 g(t− τ)∆u(τ)dτ + aut|ut| = b|u|u, in Ω× (0,∞) and showed, under suitable conditions on g, that solutions with negative energy blow up in finite time if γ > m, and continue to exist if m ≥ γ.”
Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation (2006, methodology): “Concerning nonexistence, Messaoudi [ 17 ] showed that Todorova and Georgiev’s results can be extended to (1.1) using the technique of [7] with a modification in the energy functional due to the different nature of the problems.”
A Blow-Up Result in a Nonlinear Wave Equation with Delay (2016, unknown): “In [14], Messaoudi considered the following initial-boundary value problem in the presence of the viscoelastic term ⎧ ⎪⎨ ⎪⎩ utt −Δu+ ∫ t 0 g(t− τ)Δu(τ)dτ + ut|ut|m−2 = u|u|p−2, in Ω× (0,∞) u(x, t) = 0, x ∈ ∂Ω, t ≥ 0 u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, (1.”