RT Journal Article
T1 The Cauchy problem for ut = Δu(m) when 0<m<1
A1 Herrero, Miguel A.
A1 Pierre, Michel
AB 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).
PB American Mathematical Society
SN 0002-9947
YR 1985
FD 1985-09
LK https://hdl.handle.net/20.500.14352/64723
UL https://hdl.handle.net/20.500.14352/64723
LA eng
DS Docta Complutense
RD 9 may 2025