摘要 : This paper deals with a parabolic p(x)-Laplace equation with absorption and nonlocal source. Firstly, we study the uniqueness and existence of weak solutions in some Sobolev spaces with variable exponents. Secondly, by using some ... 展开 This paper deals with a parabolic p(x)-Laplace equation with absorption and nonlocal source. Firstly, we study the uniqueness and existence of weak solutions in some Sobolev spaces with variable exponents. Secondly, by using some kinds of ordinary differential inequalities, we obtain the extinction and non-extinction criteria for weak solutions, where the extinction rate is given also. Thirdly, we use the auxiliary function methods and different embedding inequalities to classify blow-up and global existence of solutions under some conditions on the initial data and the diffusion coefficient. Moreover, the estimates on blow-up time and rates of weak solutions and large time behavior of global solutions are studied, respectively. 收起