Solutions of the 4-species quadratic reaction-diffusion system are bounded and C ∞ -smooth, in any space dimension

Caputo Cristina 1 Thierry Goudon 2 Alexis Vasseur 1
2 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : We establish the boundedness of solutions of reaction-diffusion systems with qua-dratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N > 2. This bound imply the C ∞-regularity of the solutions. This result extends the theory which was restricted to the two-dimensional case. The proof heavily uses De Giorgi's iteration scheme, which allows us to obtain local estimates. The arguments relies on duality reasonings in order to obtain new estimates on the total mass of the system, both in L (N +1)/N norm and in a suitable weak norm. The latter uses C α regularization properties for parabolic equations.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.inria.fr/hal-01588779
Contributor : Thierry Goudon <>
Submitted on : Sunday, September 17, 2017 - 1:36:49 AM
Last modification on : Tuesday, June 19, 2018 - 10:07:38 AM
Long-term archiving on : Monday, December 18, 2017 - 12:30:32 PM

File

CaGoVa.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01588779, version 1

Citation

Caputo Cristina, Thierry Goudon, Alexis Vasseur. Solutions of the 4-species quadratic reaction-diffusion system are bounded and C ∞ -smooth, in any space dimension. 2017. ⟨hal-01588779⟩

Share

Metrics

Record views

333

Files downloads

104