Diffusion versus absorption in semilinear elliptic equations

Andrey Shishkov (1) , Laurent Veron (2)

1 IAMM - Institute of Applied Mathematics and Mechanics of NAS of Ukraine
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study the limit behaviour of a sequence of singular solutions of a nonlinear elliptic equation with a strongly degenerate absorption term at the boundary of the domain. We give sharp conditions on the level of degeneracy in order the pointwise singularity not to propagate along the boundary.

Mots clés: Elliptic equations; energy estimates; Saint Venant principle

Domaines: Equations aux dérivées partielles [math.AP]

Andrey Shishkov, Laurent Veron. Diffusion versus absorption in semilinear elliptic equations. Journal of Mathematical Analysis and Applications, 2009, 352, pp.206-217. ⟨hal-00282483⟩