Local and global strong solution by the semi-Galerkin method for the model of mass diffusion

Abstract

In this work, we present some results for local and global in time solutions (defined in the time interval (0, T) with T < +∞ or T = +∞) for the model of mass diffusion by using the spectral semi-Galerkin approximations. We establish results related to the global existence of weak solutions, to the existence of strong solutions (local in time or global in time for small enough data in 3D domains or general data in 2D case), to the regularity of strong solutions and the effects of the exponential decay of the external force in the asymptotic behavior when t → +∞ for global solutions.