Abstract
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 on an a priori dimension-independent L2-estimate, valid for a wider class of systems including also some classical Lotka-Volterra systems, and which provides an L1-bound on the nonlinearities, at least for not too degenerate diffusions. In the more degenerate case, some global existence may be stated with the use of a weaker notion of renormalized solution with defect measure, arising in the theory of kinetic equations.
Keywords: reaction-diffusion system; Lotka-Volterra systems; weak solutions; renormalized solutions; global existence; entropy methods
Published Online: 2016-03-10
Published in Print: 2007-08-01
© 2016 by Advanced Nonlinear Studies, Inc.
