On the evolution p-Laplacian with nonlocal memory

We study the homogeneous Dirichlet problem for the evolution p-Laplacian with the nonlocal memory term (0.1)ut−Δpu=∫0tg(t−s)Δpu(x,s)ds+Θ(x,t,u)+f(x,t)in  Q=Ω×(0,T),  where Ω⊂Rn is a bounded domain, Θ, g and f are given functions. It is proved that for max{1,2nn+2}

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Bibliographic Details
Published in:Nonlinear analysis 2016-03, Vol.134, p.31-54
Main Authors: Antontsev, Stanislav, Shmarev, Sergey, Simsen, Jacson, Simsen, Mariza S.
Format: Article
Language:English
Subjects:
Evolution [formula omitted]-Laplacian
Finite speed of propagation
Nonlocal equation
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Summary:We study the homogeneous Dirichlet problem for the evolution p-Laplacian with the nonlocal memory term (0.1)ut−Δpu=∫0tg(t−s)Δpu(x,s)ds+Θ(x,t,u)+f(x,t)in  Q=Ω×(0,T),  where Ω⊂Rn is a bounded domain, Θ, g and f are given functions. It is proved that for max{1,2nn+2}
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.12.011