Convergence of the Dirichlet solutions of the very fast diffusion equation Original Research Article

For any −10t>0, u(x,0)=u0(x)u(x,0)=u0(x) in (−R,R)(−R,R), converges uniformly on every compact subset of R×(0,T)R×(0,T) to the solution of the equation ut=(um/m)xxut=(um/m)xx in R×(0,T)R×(0,T), u(x,0)=u0(x)u(x,0)=u0(x) in RR, which satisfies some mass loss formula on (0,T)(0,T) where TT is the maximal time such that the solution uu is positive. We also prove that the solution constructed is equal to the solution constructed in Hui (2007) [15] using approximation by solutions of the corresponding Neumann problem in bounded cylindrical domains.