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We study the uniform boundedness of solutions to reaction-diffusion systemspossessing a Lyapunov-like function and satisfying an {\it intermediate sumcondition}. This significantly generalizes the mass dissipation condition inthe literature and thus allows the nonlinearities to have arbitrary polynomialgrowth. We show that two dimensional reaction-diffusion systems, with quadraticintermediate sum conditions, have global solutions which are bounded uniformlyin time. In higher dimension, bounded solutions are obtained under thecondition that the diffusion coefficients are {\it quasi-uniform}, i.e. theyare close to each other. Applications include boundedness of solutions tochemical reaction networks with diffusion.

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