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

Meilan Qiu, Liquan Mei

Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, China.
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China.

DOI: 10.4236/apm.2013.31A028                

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 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.

Keywords

Weighted Sobolev Space; Energy Estimates; Compact Imbedding; Sobolev Interpolation Inequalities

Conflicts of Interest

The authors declare no conflicts of interest.

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