Pointwisea priori bounds for a strongly coupled system of reaction-diffusion equations with a balance law
Jacob Isaac Kanel, Mokhtar Kirane · Mathematical Methods in the Applied Sciences · 1998
We consider a reaction–diffusion system with a full matrix of diffusion coefficients satisfying a balance law on a bounded domain with no-flux boundary conditions. We demonstrate that global solutions exist for polynomial reaction terms provided some conditions on the diffusion coefficients are satisfied. The proof makes use of comparison results and Solonnikov's estimates concerning linear parabolic equations in Banach spaces. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.