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Existence of Weak Solutions for a Class of Quasilinear Parabolic Problems in Weighted Sobolev Space

Author(s): Meilan Qiu | Liquan Mei

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 01;
Start page: 204;
Date: 2013;
Original page

Keywords: Weighted Sobolev Space | Energy Estimates | Compact Imbedding | Sobolev Interpolation Inequalities

In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the compact imbedding in weighted Sobolev space and extending Galerkin’s method to a new class of nonlinear problems, we drive out that there exists at least one weak solution of the nonlinear equations in the interval [0,T] for the fixed time T>0.
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