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2019 Solutions of the 4-species quadratic reaction-diffusion system are bounded and $C^\infty$-smooth, in any space dimension
M. Cristina Caputo, Thierry Goudon, Alexis F. Vasseur
Anal. PDE 12(7): 1773-1804 (2019). DOI: 10.2140/apde.2019.12.1773

Abstract

We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly superquadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N>2. This bound implies 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 rely on duality reasoning in order to obtain new estimates on the total mass of the system, both in the L(N+1)N norm and in a suitable weak norm. The latter uses Cα regularization properties for parabolic equations.

Citation

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M. Cristina Caputo. Thierry Goudon. Alexis F. Vasseur. "Solutions of the 4-species quadratic reaction-diffusion system are bounded and $C^\infty$-smooth, in any space dimension." Anal. PDE 12 (7) 1773 - 1804, 2019. https://doi.org/10.2140/apde.2019.12.1773

Information

Received: 28 November 2017; Revised: 22 August 2018; Accepted: 25 October 2018; Published: 2019
First available in Project Euclid: 31 July 2019

zbMATH: 07115634
MathSciNet: MR3986541
Digital Object Identifier: 10.2140/apde.2019.12.1773

Subjects:
Primary: 35B65, 35K45, 35K57

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 7 • 2019
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