Abstract:

In this paper, we mainly discuss an important class of nonclassical diffusion equation which the additional damping terms

vary over time. The existence of global weak solution is obtained by using the method of Faedo-Galerkin and analytical techniques. Meanwhile, we also prove the uniqueness of the solution and the continuous dependence on initial value, where the nonlinearity f satisfies arbitrary polynomial growth.

Key words: Nonclassical diffusion equation ,  Global weak solution , Arbitrary polynomial growth ,  Galerkin's method