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

Abstract

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 Galerkins 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 T0.

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M. Qiu and L. Mei, "Existence of Weak Solutions for a Class of Quasilinear Parabolic Problems in Weighted Sobolev Space," Advances in Pure Mathematics, Vol. 3 No. 1A, 2013, pp. 204-208. doi: 10.4236/apm.2013.31A028.

Conflicts of Interest

The authors declare no conflicts of interest.

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