Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations



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Díaz Díaz, Jesús Ildefonso and 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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Official URL: 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.

Item Type:Article
Uncontrolled Keywords:Pointwise gradient estimates, One-dimensional parabolic equations, Non linear diffusion-convection equation, Regularizing effects, Unilateral estimates, Interfaces
Subjects:Sciences > Mathematics > Differential equations
ID Code:12463
Deposited On:23 Mar 2011 15:29
Last Modified:12 Dec 2018 15:07

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