Regularity and solution profiles along propagation for a cooperative species system with non-linear diffusion

• Published in: Journal of applied mathematics & computing Vol. 68; no. 4; pp. 2215 - 2233
• Main Author: Palencia, José Luis Díaz
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022; Springer Nature B.V
• Subjects: Applied mathematics; Computational Mathematics and Numerical Analysis; Exact solutions; Linear operators; Mathematical analysis; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; Propagation; Regularity; Species diffusion; Theory of Computation; Absorption; Non-linearity; Coupled system; Cooperation; 35K59; Reaction; Diffusion; 35K57; 35K55; 35K65
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-021-01616-8

The present analysis provides insights and analytical findings for a cooperative system formulated with non-linear diffusion. This work discusses, from an analytical perspective, the interaction of two species when both cooperate to explore new territories. Firstly, the analysis focuses on regularity, existence and uniqueness of weak solutions considering slightly positivity in the non-linear operator together with a monotone argument in the independent terms. Afterwards, analytical solution profiles are provided making use of selfsimilar solutions. Non-linear diffusion induces the existence of a propagating front and determines the property of finite speed of propagation in both species when they cooperate to explore new territories.