Regularization and propagation in the heat equation for infinite-dimensional Hilbert spaces

Abstract

This paper deals with the mathematical analysis of the heat equation in infinite- dimensional Hilbert spaces. Specifically some regularization properties and propagation results are investigated. The mathematical investigations are based on some methods proposed in the literature by P. L. Lions and coworkers. In particular Hilbert-Schmidt operators, Faedo- Galerkin approximate method, B-modulus continuity arguments and weakly continuity hypothesis are employed. A result on the stability with respect to the uniform convergence topology is also presented.