scholarly journals Trend to equilibrium of renormalized solutions to reaction–cross-diffusion systems

2019 ◽  
Vol 88 ◽  
pp. 81-89
Author(s):  
Esther S. Daus ◽  
Bao Quoc Tang
Keyword(s):  
Reaction Cross ◽  
Renormalized Solutions ◽  
Cross Diffusion ◽  
Diffusion Systems

scholarly journals Weak–strong uniqueness of renormalized solutions to reaction–cross-diffusion systems

2019 ◽  
Vol 29 (02) ◽  
pp. 237-270 ◽  
Author(s):  
Xiuqing Chen ◽  
Ansgar Jüngel
Keyword(s):  
Strong Solution ◽  
Gradient Flow ◽  
Growth Conditions ◽  
Reaction Cross ◽  
Strong Uniqueness ◽  
Renormalized Solutions ◽  
Renormalized Solution ◽  
Cross Diffusion ◽  
Diffusion Systems ◽  
Flux Boundary Conditions

The weak–strong uniqueness for renormalized solutions to reaction–cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada–Kawasaki–Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based on the evolution of the relative entropy modified by suitable cutoff functions.

scholarly journals Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems

2018 ◽  
Vol 50 (5) ◽  
pp. 5695-5718 ◽  
Author(s):  
J. A. Carrillo ◽  
S. Fagioli ◽  
F. Santambrogio ◽  
M. Schmidtchen
Keyword(s):  
Reaction Cross ◽  
Splitting Schemes ◽  
Cross Diffusion ◽  
Diffusion Systems

scholarly journals On the Entropic Structure of Reaction-Cross Diffusion Systems

2015 ◽  
Vol 40 (9) ◽  
pp. 1705-1747 ◽  
Author(s):  
L. Desvillettes ◽  
T. Lepoutre ◽  
A. Moussa ◽  
A. Trescases
Keyword(s):  
Reaction Cross ◽  
Cross Diffusion ◽  
Diffusion Systems

scholarly journals Lumped finite elements for reaction–cross-diffusion systems on stationary surfaces

2017 ◽  
Vol 74 (12) ◽  
pp. 3008-3023 ◽  
Author(s):  
Massimo Frittelli ◽  
Anotida Madzvamuse ◽  
Ivonne Sgura ◽  
Chandrasekhar Venkataraman
Keyword(s):  
Finite Elements ◽  
Reaction Cross ◽  
Cross Diffusion ◽  
Diffusion Systems
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