Article
Ufa Mathematical Journal
Volume 3, Number 3, pp. 3-14
The lower estimate of decay rate of solution for doubly nonlinear parabolic equation
Andriyanova E.R., Mukminov F.Kh.
Download PDF
Article on MathNetAbstact
Existence of strong solution to doubly nonlinear parabolic equation is established on unbounded domains by the method of Galerkin's approximations. In early papers existence was proved usually on bounded domains by approximating the evolution part of equation with finite differences. Usage of Galerkin's approximations make possible to prove the second integral identity. Basing on the identity the bottom estimate of decay rate of solution norm is proved on bounded domains. Early an analogous estimates for quasilinear parabolic equation were established by Tedeev A.F. and Alikakos N., Rostmanian R.