The balance between diffusion and absorption in semilinear parabolic equations

  • Andrey Shishkov

    Academy of Sciences of Ukraine, Donetsk, Ukraine
  • Laurent Véron

    Université François Rabelais, Tours, France

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