L^1 convergence toward Barenblatt solution of isentropic porous medium flows

PDE Seminar
Tuesday, February 9, 2010 - 15:00
1 hour (actually 50 minutes)
Skiles 255
Georgia Tech
 Darcy's law was observed in the motion of porous medium flows. This talk aims at the mathematical justification on Darcy's law as long time limit from compressible Euler equations with damping. In particularly, we shall showthat any physical solution with finite total mass shall converges in L^1 distance toward the Barenblatt's solution of the same mass for the Porous Medium Equation. The approach will explore the dissipation of the entropy inequality motivated by the second law of thermodynamics. This is a joint work with Feimin Huang and Zhen Wang.