Herrero, Miguel A.Pierre, Michel2023-06-212023-06-211985-090002-994710.2307/1999900https://hdl.handle.net/20.500.14352/64723This 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).engjournal articlehttp://www.ams.org/journals/tran/1985-291-01/S0002-9947-1985-0797051-0/S0002-9947-1985-0797051-0.pdfhttp://www.ams.orgrestricted access517.955517.9Cauchy problemnonlinear diffusioninitial-value problemregularizing effects.Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias