%0 Book Section
%T On the limit of solutions of ut=Δum as m→∞
publisher Libreria Editrice Universitaria Levrotto & Bella
%D 1989
%U 0373-1243
%@ https://hdl.handle.net/20.500.14352/60767
%X Let f∈L1(RN), N≥1, f≥0, and consider the Cauchy problem ut=Δum on ]0,∞[×RN, u(0,⋅)=f on RN. The authors prove that as m→∞, the corresponding solutions um(t)→u_=f+Δw in L1(RN), uniformly for t in a compact set in ]0,∞[, where 0≤w_∈L1(Rn) is the solution of the variational inequality Δw_∈L1(RN), 0≤f+Δw_≤1, w_(f+Δw_ −1)=0 a.e. The authors also show similar results for the same equation on a bounded open set Ω in RN with Dirichlet or Neumann boundary conditions
%~