Asymptotic convergence of solutions for Laplace reaction–diffusion equations. (February 2020)

• Record Type: Journal Article
• Authors: Iwasaki, Satoru; Yagi, Atsushi
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Diffusion equations in composite media -- Łojasiewicz–Simon inequality -- Asymptotic convergence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.102986
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the initial–boundary value problem for a Laplace reaction–diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show asymptotic convergence of bounded global solutions if they exist under the assumption that the reaction function is analytic in neighborhoods of their ω -limit sets. Reduction of degenerate evolution equation to multivalued evolution equation enables us to use the theory of the infinite-dimensional Łojasiewicz–Simon gradient inequality.