Special Session 102: 

Existence of solutions with moving singularities for equations of porous medium type

Jin Takahashi
Tokyo Institute of Technology
Japan
Co-Author(s):    
Abstract:
We consider singular solutions for equations of porous medium type $u_t=\Delta u^m$ ($m>0$). Under some restriction on the range of $m$ and some smallness assumption on the velocity of the singular point, we prove that there exists a solution with a moving singularity for the equations. This talk is based on a joint work with Professor Marek Fila (Comenius University) and Professor Eiji Yanagida (Tokyo Institute of Technology).