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On the Cauchy problem and initial traces for a degenerate parabolic equation

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Di Benedetto, E. y Herrero, Miguel A. (1989) On the Cauchy problem and initial traces for a degenerate parabolic equation. Transactions of the American Mathematical Society, 314 (1). pp. 187-224. ISSN 0002-9947

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URL Oficial: http://www.ams.org/journals/tran/1989-314-01/S0002-9947-1989-0962278-5/S0002-9947-1989-0962278-5.pdf


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The authors study the Cauchy problem for the degenerate parabolic equation ut = div(|Du| p−2 Du)(p<2), and find sufficient conditions on the initial trace u0 (and in particular on its behaviour as |x|→∞) for existence of a solution in some strip RN × (0,T). Using a Harnack type inequality they show that these conditions are optimal in the case of nonnegative solutions. Uniqueness of solutions is shown if u0 belongs to L1loc(RN), but is left open in the case that u0 is merely a locally bounded measure. The results are closely related to papers by Aronson-Caffarelli, Benilan-Crandall-Pierre, and Dahlberg-Kenig about the porous medium equation ut = Δum. The proofs are different and allow one to generalize some of the above results to equations with variable coefficients.


Tipo de documento:Artículo
Palabras clave:Cauchy problem; porous medium equation; existence; Harnack-type inequality; Uniqueness
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:17482
Depositado:18 Dic 2012 09:32
Última Modificación:27 Jun 2018 11:39

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