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Entropy 2016, 18(11), 413; doi:10.3390/e18110413

Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces

1
School of Science, Dalian Jiaotong University, Dalian 116028, China
2
Department of Mathematics, Dalian Nationalities University, Dalian 116600, China
*
Author to whom correspondence should be addressed.
Academic Editor: Angelo Plastino
Received: 17 September 2016 / Revised: 12 November 2016 / Accepted: 15 November 2016 / Published: 18 November 2016
View Full-Text   |   Download PDF [258 KB, uploaded 18 November 2016]

Abstract

This paper is devoted to studying the existence and uniqueness of weak solutions for an initial boundary problem of a nonlinear fourth-order parabolic equation with variable exponent v t + div ( | v | p ( x ) 2 v ) | v | q ( x ) 2 v = g ( x , v ) . By applying Leray-Schauder’s fixed point theorem, the existence of weak solutions of the elliptic problem is given. Furthermore, the semi-discrete method yields the existence of weak solutions of the corresponding parabolic problem by constructing two approximate solutions. View Full-Text
Keywords: fourth-order parabolic equation; semi-discretization; variable exponent fourth-order parabolic equation; semi-discretization; variable exponent
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liang, B.; Peng, X.; Qu, C. Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces. Entropy 2016, 18, 413.

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