The blow-up of solutions for m-Laplacian equations with variable sources under positive initial energy

This paper deals with homogeneous Dirichlet boundary value problem to a class of m-Laplace equations with variable reaction ∂u∂t−div(|∇u|m−2∇u)=uq(x),x∈Ω,t>0, the bounded domain Ω⊂RN(N≥1) with a smooth boundary. We prove that the weak solutions of the above problems blow up in finite time for all...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2016-11, Vol.72 (9), p.2516-2524
Main Author: Wu, Xiulan
Format: Article
Language:English
Subjects:
[formula omitted]-Laplace equations
Blow up
Boundary conditions
Boundary value problems
Dirichlet problem
Laplace equation
Positive initial energy
Smooth boundaries
Variable source
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Summary:This paper deals with homogeneous Dirichlet boundary value problem to a class of m-Laplace equations with variable reaction ∂u∂t−div(|∇u|m−2∇u)=uq(x),x∈Ω,t>0, the bounded domain Ω⊂RN(N≥1) with a smooth boundary. We prove that the weak solutions of the above problems blow up in finite time for all q−>m−1(m≥2), when the initial energy is positive and initial data is suitably large. This result improves the recent result by Zhou and Yang (2015), which asserts the blow-up of solutions for N>m, provided that q+
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2016.09.015