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On the limit of solutions of ut=Δum as m→∞

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Bénilan, Philippe and Boccardo, L. and Herrero, Miguel A. (1989) On the limit of solutions of ut=Δum as m→∞. In Some topics in nonlinear PDEs. Università e Politecnico di Torino. Seminario Matematico. Rendiconti (47, Sp). Libreria Editrice Universitaria Levrotto & Bella, Torino, pp. 1-13. ISBN 0373-1243

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Abstract

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


Item Type:Book Section
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Proceedings of the conference held in Turin, October 2–6, 1989

Subjects:Sciences > Mathematics > Differential equations
ID Code:22719
Deposited On:05 Sep 2013 16:04
Last Modified:02 Sep 2020 07:04

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