Blow-up and propagation of disturbances for fast diffusion equations |
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Authors: | Paul-Emile Maing |
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Affiliation: | aGRIMMAG, Université des Antilles-Guyane, Département Scientifique Interfacultaire, Campus de Schoelcher, 97230 Cedex, Martinique, France |
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Abstract: | This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1 in RN (N≥1), where m∈(0,1), p1>1 and α>0. The initial condition u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0 so that u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x) for small enough values of t>0. |
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Keywords: | Fast diffusion Finite blow-up time Cauchy problem |
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