%0 Journal Article
%A Herrero, Miguel A.
%A Pierre, Michel
%T The Cauchy problem for ut = Δu(m) when 0<m<1
%D 1985
%@ 0002-9947
%U https://hdl.handle.net/20.500.14352/64723
%X This paper deals with the Cauchy problem for the nonlinear diffusion equation ∂u/∂t - Δ (u|u|m+1) = 0 on (0, ∞) x RN,u(0, .) = u0 when 0 < m < 1 (fast diffusion case). We prove that there exists a global time solution for any locally integrable function u0: hence, no growth condition at infinity for u0 is required. Moreover the solution is shown to be unique in that class. Behavior at infinity of the solution and L∞loc-regularizing effects are also examined when m Є (max{(N-2)/N, 0}, 1).
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