Existence of solutions for a nonlocal reaction-diffusion equation in biomedical applications

Abstract

The paper is devoted to a nonlocal semi-linear elliptic equation in R n arising in various biological and biomedical applications. The Fredholm property studied for the corresponding linear elliptic operators with discontinuous coefficients allows the application of the implicit function theorem to prove the persistence of solutions under a small perturbation of the problem. Furthermore, the existence of solutions is established by the Leray-Schauder method based on the topological degree for Fredholm and proper operators and on a priori estimates of solutions in some special weighted spaces.

Viral Infection Spreading in Cell Culture with Intracellular Regulation

“…The progression of viral infections in the respiratory tract can also be described as a reaction-diffusion wave, but its propagation is influenced by the airway liquids (mucus and periciliary fluid) [17]. Mathematical questions of the existence of reaction-diffusion waves describing infection spreading in its interaction with the immune response are studied in [18,19].…”