Equilibration of renormalised solutions to nonlinear chemical reaction-diffusion systems - TIB AV-Portal

Equilibration of renormalised solutions to nonlinear chemical reaction-diffusion systems

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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Fellner, Klemens

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Title

Equilibration of renormalised solutions to nonlinear chemical reaction-diffusion systems

Title of Series

Entropies, the Geometry of Nonlinear Flows, and their Applications (18w5069)

Number of Parts

31

Author

Fellner, Klemens

Contributors

Desvillettes, Laurent

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/59174 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

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Subject Area

Life Sciences Mathematics Physics

Genre

Workshop/Interactive Format Lecture

Abstract

We prove exponential convergence to equilibrium for renormalised solutions to general complex balanced reaction-diffusion systems without boundary equilibria and even for systems with boundary equilibria provided a finite dimensional inequality holds along solutions trajectories. Our proofs are based on the entropy method and represent the most general results on the convergence to equilibrium for complex balanced RD systems currently available.

Series

Entropies, the Geometry of Nonlinear Flows, and their Applications (18w5069)15 / 31

1

35:34

Phase transitions for the McKean-Vlasov equation on the torus

2

44:08

On a new proof of the Harris ergodic theorem and related subexponential convergence results

3

35:34

Super Ricci flows for weighted graphs and Markov chains

4

33:30

Stein kernels, optimal transport and the CLT

5

38:49

When Otto meets Newton and Schrödinger, an heuristic point of view

6

26:53

Existence of ground states for aggregation-diffusion equations

7

32:01

Recent results on nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics

8

32:13

Deterministic particle approximations for transport models with nonlinear mobility

9

30:42

Gradient Flows in Abstract Metric Spaces: Evolution Variational Inequalities and Stability

10

33:30

Gromov-Hausdorff convergence of discrete optimal transport

11

51:07

Entropic optimal transport and nonlinear PDE's

12

30:46

A BDF2-Approach for the Non-Linear Fokker-Planck Equation

13

26:42

Asymptotical analysis of a weighted very fast diffusion equation arising in quantization of measures via the JKO scheme

14

50:01

Global estimates for local and nonlocal porous medium type equations on bounded domains

15

40:09

Equilibration of renormalised solutions to nonlinear chemical reaction-diffusion systems

16

29:48

Hypocoercivity in Phi-entropy for linear relaxation Boltzmann equation

17

33:15

Entropy production inequalities for the Kac Walk

18

50:24

Why in some cases the asymptotic linearized problem yields optimal results for a nonlinear version of the carré du champ

19

31:02

Long time behaviour of kinetic Langevin equation

20

41:19

From Monge Transport to Skorokhod Embeddings

21

46:38

A partial Laplacian as an infinitesimal generator on the Wasserstein space

22

46:23

Entropic concavity and positive energy

23

29:50

Entropic regularization of optimal transport and applications

24

30:33

Enhancement of biological reaction by chemotaxis

25

28:18

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system

26

34:17

A new continuum theory for incompressible swelling materials

27

15:01

Wasserstein estimates and macroscopic limits in a model from ecology

28

33:39

Entropy and the Kac Master Equation

29

34:14

Towards a gradient flow for microstructure: microstructure meets Boltzmann

30

33:15

Minimizers and gradient flows in the slow diffusion limit

31

31:36

Large-time behavior in hypocoercive BGK-models

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