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Open AccessArticle

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
Entropy 2016, 18(11), 413; https://doi.org/10.3390/e18110413
Received: 17 September 2016 / Revised: 12 November 2016 / Accepted: 15 November 2016 / Published: 18 November 2016
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
MDPI and ACS Style

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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