Fundamental solutions and decay of fully non-local problems
Juan C. Pozo, Vicente Vergara · Discrete and Continuous Dynamical Systems · 2018
In this paper, we study a fully non-local reaction-diffusion equation which is non-local both in time and space. We apply subordination principles to construct the fundamental solutions of this problem, which we use to find a representation of the mild solutions. Moreover, using techniques of Harmonic Analysis and Fourier Multipliers, we obtain the temporal decay rates for the mild solutions.