Fundamental solutions and decay of fully non-local problems

By Juan C. Pozo, Vicente Vergara. Discrete and Continuous Dynamical Systems. Series A, 2018

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

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