Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

The Aronson-Bénilan Estimate in Lebesgue Spaces

Abstract : In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and Bénilan estimate in L p spaces, of some modifications and improvements, as well as to show certain limitations of their strategy.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [65 references]  Display  Hide  Download

https://hal.inria.fr/hal-02909140
Contributor : Markus Schmidtchen <>
Submitted on : Thursday, July 30, 2020 - 9:29:53 AM
Last modification on : Wednesday, June 2, 2021 - 4:26:58 PM
Long-term archiving on: : Tuesday, December 1, 2020 - 7:43:02 PM

File

final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02909140, version 1

Citation

Giulia Bevilacqua, Benoît Perthame, Markus Schmidtchen. The Aronson-Bénilan Estimate in Lebesgue Spaces. 2020. ⟨hal-02909140⟩

Share

Metrics

Record views

83

Files downloads

277