Singular limit of solutions of the porous medium type equation

Kin Ming Hui Institute of Mathematics Academia Sinica Taipei, Taiwan

              kmhui@pde.math.sinica.edu.tw

In this talk we will discuss some of our recent results on the singular limit of solutions of the porous medium type equations. In particular we will show that as m → ∞ or p → ∞ the solutions of u_{t} = Δu^{m} − u^{p}, (x, t) ∈ R^{n} × (0, T), T > 0, m > 1, p > 1, u ≥ 0, u(x, 0) = f(x) ∈ L^{1}(R^{n}) ∩ L^{∞}(R^{n}) will converge to some function.