Isolated singularities and asymptotic behaviour of the solutions of a semi-linear heat equation

Article type: Research Article

Authors: Moutoussamy, I. | Veron, L.

Affiliations: Département de Mathématiques, Faculté des Sciences, BP6759, 45067 Orleans Cedex 2, France | Département de Mathématiques et Informatique Scientifique, Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France

Abstract: We study here the limit properties of the solutions of the following singular problem (1) ut−Δu+u|u|p−l=0 in RN×R+\{(0,0)} with u(x,0)=0 if x≠(0,0). We transform the equation from an autonomous dynamical system into a weighted Sobolev space and look for the limit set of a trajectory of such a system. By using an energy method, we obtain a theorem of classification of singularities of the solutions of (1). By using the same methods we study the asymptotic behaviour of the solutions and some global singular solutions.

DOI: 10.3233/ASY-1994-9303

Journal: Asymptotic Analysis, vol. 9, no. 3, pp. 259-289, 1994