The lower estimate of decay rate of solutions for doubly nonlinear parabolic equations

Existence of strong solution to doubly nonlinear parabolic equation is established on unbounded domains by the method of Galerkin's approximations. In early publications existence was proved usually on bounded domains by approximating the evolution part of the equation by finite differences. Usage of Galerkin's approximations makes it possible to prove the second integral identity. On the basis of the identity, the bottom estimate of decay rate of the solution norm is proved on bounded domains. Similar estimates for quasilinear parabolic equations were established earlier by Tedeev A. F. and Alikakos N., Rostmanian R.