Qualitative properties of coexistence and semi-trivial limit profiles of nonautonomous nonlinear parabolic Dirichlet systems. (January 2016)

• Record Type: Journal Article
• Authors: Saldaña, Alberto
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 31
• Page End: 46
• Publication Date: 2016-01
• Subjects: primary 35K51 -- secondary 35B40; Lotka–Volterra systems -- Competition -- Rotating plane method; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.09.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the symmetry properties of limit profiles of nonautonomous nonlinear parabolic systems with Dirichlet boundary conditions in radial bounded domains. In the case of competitive systems, we show that if the initial profiles satisfy a reflectional inequality with respect to a hyperplane, then all limit profiles are foliated Schwarz symmetric with respect to antipodal points. One of the main ingredients in the proof is a new parabolic version of Serrin's boundary point lemma. Results on radial symmetry of semi-trivial profiles are discussed also for noncompetitive systems.