Singular limit of solutions of the porous medium equation with absorption
Kin Ming Hui · Transactions of the American Mathematical Society · 1998
We prove that as m → ∞ m\to \infty the solutions u ( m ) u^{(m)} of u t = Δ u m − u p u_{t}=\Delta u^{m}-u^{p} , ( x , t ) ∈ R n × ( 0 , T ) (x,t)\in R^{n}\times (0,T) , T > 0 T>0 , m > 1 m>1 , p > 1 p>1 , u ≥ 0 u\ge 0 , u ( x , 0 ) = f ( x ) ∈ L 1 ( R n