Existence of Weak Solutions for a Class of Quasilinear Parabolic Problems in Weighted Sobolev Space - Advances in Pure Mathematics

APM > Vol.3 No.1, January 2013

Advances in Pure Mathematics

Volume 3, Issue 1 (January 2013)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

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

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DOI: 10.4236/apm.2013.31A028 4,132 Downloads 7,694 Views Citations

Author(s)

Meilan Qiu, Liquan Mei

Affiliation(s)

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

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

Share and Cite:

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.

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