Boundedness for reaction-diffusion systems with Lyapunov functions and intermediate sum conditions

Abstract

We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the literature and thus allows the nonlinearities to have arbitrary polynomial growth. We show that two dimensional reaction-diffusion systems, with quadratic intermediate sum conditions, have global solutions which are bounded uniformly in time. In higher dimension, bounded solutions are obtained under the condition that the diffusion coefficients are {\it quasi-uniform}, i.e. they are close to each other. Applications include boundedness of solutions to chemical reaction networks with diffusion.

References in corpus (4)

• Improved duality estimates and applications to reaction-diffusion equations
• Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction-diffusion systems
• Close-to-equilibrium behaviour of quadratic reaction-diffusion systems with detailed balance
• Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria

Cited by in corpus (4)

• Quantitative dynamics of irreversible enzyme reaction-diffusion systems
• Global well-posedness and nonlinear stability of a chemotaxis system modeling multiple sclerosis
• Analysis of mass controlled reaction-diffusion systems with nonlinearities having critical growth rates
• Reaction-Diffusion-Advection Systems with Discontinuous Diffusion and Mass Control