Weak solutions for nonlocal evolution variational inequalities involving gradient constraints and variable exponent

• Main Authors: Mingqi Xiang, Yongqiang Fu
• Format: Article
• Language: English
• Published: Texas State University 2013-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Nonlocal evolution variational inequality; variable exponent space; Galerkin approximation; penalty method
• Online Access: http://ejde.math.txstate.edu/Volumes/2013/100/abstr.html

In this article, we study a class of nonlocal quasilinear parabolic variational inequality involving $p(x)$-Laplacian operator and gradient constraint on a bounded domain. Choosing a special penalty functional according to the gradient constraint, we transform the variational inequality to a parabolic equation. By means of Galerkin's approximation method, we obtain the existence of weak solutions for this equation, and then through a priori estimates, we obtain the weak solutions of variational inequality.