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The Cauchy problem for ut = Δu(m) when 0<m<1

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Herrero, Miguel A. and Pierre, Michel (1985) The Cauchy problem for ut = Δu(m) when 0<m<1. Transactions of the American Mathematical Society, 291 (1). pp. 145-158. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/1985-291-01/S0002-9947-1985-0797051-0/S0002-9947-1985-0797051-0.pdf


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Abstract

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).


Item Type:Article
Uncontrolled Keywords:Cauchy problem, nonlinear diffusion, initial-value problem, regularizing effects.
Subjects:Sciences > Mathematics > Differential equations
ID Code:17623
Deposited On:11 Jan 2013 09:40
Last Modified:12 Dec 2018 15:08

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