Research On The Entropy Solution Of Parabolic P(x)-Laplacian Equation

The existence and uniqueness of entropy solutions for a class of parabolic equations involving p(x)-Laplacian operator are investigated.We first prove the existence of the global weak solution for the p(x)-Laplacian equations via the difference and variation methods as well as the standard domain expansion technique.And then,by constructing an approximate solution sequence and solving a related approximation problem,the en-tropy solution for the p(x)-Laplacian equations with irregular initial data in whole space is also obtained.