Free energy estimates and asymptotic behaviour of reaction-diffusion processes.
- Gröger, Konrad
2010 Mathematics Subject Classification
- 35K57 35K55 35K45
- Reaction-diffusion systems, asymptotic behaviour, Lyapunov function
We prove a class of inequalities closely related to Poincaré's Inequality. Roughly speaking, these inequalites state for many reaction-diffusion systems the free energy can be estimated by the corresponding dissipation rate. This allows to describe the asymptotic behaviour of such reaction-diffusion systems without using global uniform bounds for the concentrations.