[图书][B] Parabolic equations in biology

B Perthame, B Perthame - 2015 - Springer
This chapter contains a general presentation of parabolic partial differential equations that
are used in biology: Lotka-Volterra systems and chemical or enzymatic reactions. These are …

Improved duality estimates and applications to reaction-diffusion equations

JA Canizo, L Desvillettes, K Fellner - Communications in Partial …, 2014 - Taylor & Francis
We present a refined duality estimate for parabolic equations. This estimate entails new
results for systems of reaction-diffusion equations, including smoothness and exponential …

Gradient structures and geodesic convexity for reaction–diffusion systems

M Liero, A Mielke - … Transactions of the Royal Society A …, 2013 - royalsocietypublishing.org
We consider systems of reaction–diffusion equations as gradient systems with respect to an
entropy functional and a dissipation metric given in terms of a so-called Onsager operator …

Global existence for quadratic systems of reaction-diffusion

L Desvillettes, K Fellner, M Pierre… - Advanced Nonlinear …, 2007 - degruyter.com
We prove global existence in time of weak solutions to a class of quadratic reaction-diffusion
systems for which a Lyapounov structure of L log L-entropy type holds. The approach relies …

Trend to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks

L Desvillettes, K Fellner, BQ Tang - SIAM Journal on Mathematical Analysis, 2017 - SIAM
The quantitative convergence to equilibrium for reaction-diffusion systems arising from
complex balanced chemical reaction networks with mass action kinetics is studied using the …

Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems

J Fischer - Archive for Rational Mechanics and Analysis, 2015 - Springer
In the present work we introduce the notion of a renormalized solution for reaction–diffusion
systems with entropy-dissipating reactions. We establish the global existence of …

[HTML][HTML] Global classical solutions to quadratic systems with mass control in arbitrary dimensions

K Fellner, J Morgan, BQ Tang - Annales de l'Institut Henri Poincaré C …, 2020 - Elsevier
The global existence of classical solutions to reaction-diffusion systems in arbitrary space
dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly …

Regularity analysis for systems of reaction-diffusion equations

T Goudon, A Vasseur - Annales scientifiques de l'Ecole normale …, 2010 - numdam.org
R.–Ce travail est consacré à l'étude de la régularité des solutions de certains
systèmes d'équations de réaction-diffusion. En particulier, nous montrons que les solutions …

Weak–strong uniqueness of solutions to entropy-dissipating reaction–diffusion equations

J Fischer - Nonlinear Analysis, 2017 - Elsevier
We establish a weak–strong uniqueness principle for solutions to entropy-dissipating
reaction–diffusion equations: As long as a strong solution to the reaction–diffusion equation …

On uniform decay of the entropy for reaction–diffusion systems

A Mielke, J Haskovec, PA Markowich - Journal of Dynamics and …, 2015 - Springer
This work provides entropy decay estimates for classes of nonlinear reaction–diffusion
systems modeling reversible chemical reactions under the detailed-balance condition. We …