# Extinction and asymptotic behavior of solutions for nonlinear parabolic equations with variable exponent of nonlinearity

Boundary Value Problems, Jul 2013

The aim of this paper is to study the existence and extinction of weak solutions of the initial and boundary value problem for u t = div ( ( | u | σ ( x , t ) + d 0 ) | ∇ u | p ( x , t ) − 2 ∇ u ) + f ( x , t , u ) . First, the authors apply the method of parabolic regularization and Galerkin’s method to prove the existence of solutions to the problem mentioned and then obtain the comparison principle by arguing by contradiction. Furthermore, the authors prove that the solution vanishes in finite time and approaches 0 in L 2 ( Ω ) norm as t → ∞ .

This is a preview of a remote PDF: http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2013-164.pdf

Yanchao Gao, Wenjie Gao. Extinction and asymptotic behavior of solutions for nonlinear parabolic equations with variable exponent of nonlinearity, Boundary Value Problems, 2013, 164,