Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces
School of Science, Dalian Jiaotong University, Dalian 116028, China
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
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
. 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.
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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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.
Liang B, Peng X, Qu C. Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces. Entropy. 2016; 18(11):413.
Liang, Bo; Peng, Xiting; Qu, Chengyuan. 2016. "Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces." Entropy 18, no. 11: 413.
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