A nonlinear viscoelastic plate equation with $\vec{p}(x,t)$-Laplace operator: Blow up of solutions with negative initial energy Full article
| Journal |
Nonlinear Analysis: Real World Applications
ISSN: 1468-1218 |
||||||
|---|---|---|---|---|---|---|---|
| Output data | Year: 2020, Volume: 59, Pages: 103240 Pages count : 1 DOI: 10.1016/j.nonrwa.2020.103240 | ||||||
| Tags | Anisotropy; Blow up in finite time; Non-linear viscoelastic equation; Nonstandard growth conditions; Strong damping | ||||||
| Authors |
|
||||||
| Affiliations |
|
Abstract:
In this paper we consider a nonlinear class viscoelastic plate equation with a lower order by perturbation of p⃗(x,t)-Laplace operator of the form utt+Δ2u−Δp⃗(x,t)u+∫0tg(t−s)Δu(s)ds−ϵΔut+f(u)=0,(x,t)∈QT=Ω×(0,T), associated with initial and Dirichlet–Neumann boundary conditions. Under suitable conditions on g,f and the variable exponent of the p⃗(x,t)-Laplace operator, we prove a blow up in finite time with negative initial energy in the presence of a strong damping ϵΔut(ϵ>0) acting in the domain. This equation corresponds to a viscoelastic version arising in dynamics of elastoplastic flows and plate vibrations.
Cite:
Antontsev S.
, Ferreira J.
A nonlinear viscoelastic plate equation with $\vec{p}(x,t)$-Laplace operator: Blow up of solutions with negative initial energy
Nonlinear Analysis: Real World Applications. 2020. V.59. P.103240. DOI: 10.1016/j.nonrwa.2020.103240 WOS Scopus РИНЦ OpenAlex
A nonlinear viscoelastic plate equation with $\vec{p}(x,t)$-Laplace operator: Blow up of solutions with negative initial energy
Nonlinear Analysis: Real World Applications. 2020. V.59. P.103240. DOI: 10.1016/j.nonrwa.2020.103240 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000618633800005 |
| Scopus: | 2-s2.0-85096652415 |
| Elibrary: | 45125438 |
| OpenAlex: | W3107956981 |