Existence and uniqueness of very singular solutions for a fast 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

Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption \begin{equation*} \partial_t u -\Delta_{p}u+|\nabla u|^q=0, \ \hbox{in} \ (0,\infty)\times\real^N, \end{equation*} where $2N/(N+1)

Mots clés: very singular solution; singular diffusion; gradient absorption; self-similar solutions; p-Laplacian; uniqueness

Domaines: Equations aux dérivées partielles [math.AP]

Razvan Gabriel Iagar, Philippe Laurencot. Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption. Journal of the London Mathematical Society, 2013, 87, pp.509-529. ⟨10.1112/jlms/jds051⟩. ⟨hal-00606629⟩