Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations

Peiying Chen

doi:10.3934/era.2017.24.005

Article Contents

2017, Volume 24: 38-52. Doi: 10.3934/era.2017.24.005

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Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations

Peiying Chen

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received: December 15, 2016

Revised: April 29, 2017

Published: August 2017

The author would like to thank her supervisor Prof. Zhongrui Shi, who supported her throughout her paper with his knowledge, patience and excellent guidance.

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In this paper, we study the Dirichlet boundary value problem of a class of nonlinear parabolic equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.

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Mathematics Subject Classification: 35K55(Primary), 35K61(Secondary), 46B20.

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