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- Title
Existence of weak solutions for a class of parabolic problems in weighted Sobolev space.
- Authors
Ali, Khaled Ben; Ghanmi, Abdeljabbar
- Abstract
In this paper, we established the existence and uniqueness of weak solutions for some parabolic problems with nonlinear perturbation term in weighted Sobolev space. First, we investigated the compact imbedding in weighted Sobolev space, which can be imbedded compactly into H10(Ω) and L2(Ω) spaces. By exploiting Sobolev interpolation inequalities and extending Galerkin's method to a new class of nonlinear problems, we proofed the energy estimates of the equations and furthermore obtained the unique weak solution.
- Publication
Nonlinear Studies, 2016, Vol 23, Issue 2, p253
- ISSN
1359-8678
- Publication type
Academic Journal