Pointwise gradient estimates of solutions to onedimensional nonlinear
parabolic equations |
| |
Authors: | Philippe Bénilan † Jesús Ildefonso Díaz |
| |
Affiliation: | (1) Facultad de Matemáticas, Universidad Complutense de Madrid, 20040 Madrid, Spain |
| |
Abstract: | 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. |
| |
Keywords: | 35K65 35K10 35R35 76D27 |
本文献已被 SpringerLink 等数据库收录! |
|