Acta mathematica scientia, Series B >
EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF#br# NONLINEARITY
Received date: 2011-01-04
Online published: 2012-05-20
Supported by
Supported by NSFC (10771085), Graduate Innovation Fund of Jilin Univer-sity(20111034), and the 985 program of Jilin University.
The authors of this article study the existence and uniqueness of weak so-lutions of the initial-boundary value problem for ut = div((|u|σ + d0)|∇u|p(x, t)−2∇u) +f(x, t) (0 < σ < 2). They apply the method of parabolic regularization and Galerkin's method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction. The authors prove that the solution approaches 0 in L2(Ω) norm as t →∞.
GUO Bin , GAO Wen-Jie . EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF#br# NONLINEARITY[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1053 -1062 . DOI: 10.1016/S0252-9602(12)60078-2
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