Global attractors for nonclassical diffusion equations with hereditary memory and a new class of nonlinearities
Volume 119 / 2017
Annales Polonici Mathematici 119 (2017), 1-21
MSC: Primary 35B41; Secondary 45K05, 76R50, 35D30.
DOI: 10.4064/ap4015-2-2017
Published online: 17 March 2017
Abstract
We study the existence and long-time behavior in terms of existence of global attractors of weak solutions to a class of nonclassical diffusion equations with hereditary memory and a new class of nonlinearities, which contains all nonlinearities of polynomial type, Sobolev type, and even exponential type. The main novelty of our result is that no restriction on the upper growth of the nonlinearity is imposed.
