A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Audrito, Alessandro; Serra, Enrico; Tilli, Paolo
• Is Part Of: Communications in partial differential equations. Volume 46:Issue 12(2021)
• Page Start: 2268
• Page End: 2287
• Publication Date: 2021-12-02
• Subjects: A priori estimates -- minimization -- parabolic reaction-diffusion systems -- strong competition; 35B25 -- 35K57 -- 49J45; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2021.1931884
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: We study the existence of segregated solutions to a class of reaction-diffusion systems with strong interactions, arising in many physical applications. These special solutions are obtained as weak limits of minimizers of a family of perturbed functionals. We prove some a priori estimates through a minimization procedure which is nonstandard in the parabolic theory: our approach is purely variational and all the information is encoded in the family of functionals we consider.