Universidad Complutense de Madrid
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Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations



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Díaz Díaz, Jesús Ildefonso y Benilan, Philippe (2004) Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations. Journal of Evolution Equations , 3 (4). pp. 577-602. ISSN 1424-3199

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URL Oficial: http://www.springerlink.com/content/1424-3199/


We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.

Tipo de documento:Artículo
Palabras clave:Pointwise gradient estimates, One-dimensional parabolic equations, Non linear diffusion-convection equation, Regularizing effects, Unilateral estimates, Interfaces
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:12463
Depositado:23 Mar 2011 15:29
Última Modificación:12 Dic 2018 15:07

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