Let be continuous and nondecreasing, if , and be positive real numbers. We investigate the behavior when of the fundamental solutions of in satisfying . The main question is wether the limit is still a solution of the above equation with an isolated singularity at , or a solution of the associated ordinary differential equation which blows-up at .
Cite this article
Laurent Véron, Andrey Shishkov, The balance between diffusion and absorption in semilinear parabolic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 1, pp. 59–96DOI 10.4171/RLM/481