Homogenization for nonlocal evolution problems with three different smooth kernels (Q6567193)

The authors study the homogenization that occurs when one deals with nonlocal evolution problems with different nonsingular kernels that act in different domains. This paper is a natural continuation of their previous work [Discrete Contin. Dyn. Syst. 41, No. 6, 2777--2808 (2021; Zbl 1466.45001)], where the stationary case was studied. They assume that the special domain \( \Omega \) is divided into a sequence of two subdomains \( A_{n}\bigcup B_{n} \) and three different smooth kernels, one that controls the jumps from \( A_{n} \) to \( A_{n} \), a second one that controls the jumps from \( B_{ n} \) to \( B_{n} \) and a third one that governs the interactions between \( A_{n} \) and \( B_{n}.\) They also provide a probabilistic interpretation of this evolution equation in terms of a stochastic process that describes the movement of a particle that jumps in \( \Omega \) according to the three different kernels and show that the underlying process converges in distribution to a limit process associated with the limit equation.