Asymptotic behavior for a singular diffusion equation with gradient absorption

Razvan Gabriel Iagar (1) , Philippe Laurencot (2)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the large time behavior of non-negative solutions to the singular diffusion equation with gradient absorption $$ \partial_t u-\Delta_{p}u+|\nabla u|^q=0 \quad \hbox{in} \ (0,\infty)\times\real^N, $$ for $p_c:=2N/(N+1)

Mots clés: bounded measures; large time behavior; singular diffusion; gradient absorption; very singular solutions; p-Laplacian; bounded measures.

Domaines: Equations aux dérivées partielles [math.AP]

Razvan Gabriel Iagar, Philippe Laurencot. Asymptotic behavior for a singular diffusion equation with gradient absorption. Journal of Differential Equations, 2014, 256, pp.2739-2777. ⟨10.1016/j.jde.2014.01.016⟩. ⟨hal-00780928⟩