The balance between diffusion and absorption in semilinear parabolic equations
Andrey Shishkov
Academy of Sciences of Ukraine, Donetsk, UkraineLaurent Véron
Université François Rabelais, Tours, France
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Abstract
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
Andrey Shishkov, Laurent Véron, The balance between diffusion and absorption in semilinear parabolic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 1, pp. 59–96
DOI 10.4171/RLM/481