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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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Additional Information: | 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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