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

Abstract

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 vt + div(|∇4v|p(x)−2∇4v) − |4v|q(x)−24v = 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.

DOI: 10.3390/e18110413

Cite this paper

@article{Liang2016ExistenceOS, title={Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces}, author={Bo Liang and Xiting Peng and Chengyuan Qu}, journal={Entropy}, year={2016}, volume={18}, pages={413} }