A concrete realization of the slow-fast alternative for a semilinear heat equation with homogeneous Neumann boundary conditions

Advances in Nonlinear Analysis

article

Marina Ghisi¹  Massimo Gobbino¹  Alain Haraux² 

[1] Dipartimento di Matematica, Università degli Studi di Pisa;Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie

关键词: Semilinear parabolic equation;    decay rates;    slow solutions;    exponentially decaying solutions;    subsolutions and supersolutions;   

DOI  :  10.1515/anona-2016-0171

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions. It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions decaying to 0 exponentially (as time goes to infinity), and slow solutions decaying to 0 as negative powers of t . Here we provide a characterization of slow/fast solutions in terms of their sign, and we show that the set of initial data giving rise to fast solutions is a graph of codimension one in the phase space.

【 授权许可】

CC BY