Global Renormalised Solutions and Equilibration of Reaction–Diffusion Systems with Nonlinear Diffusion

Abstract The global existence of renormalised solutions and convergence to equilibrium for reaction–diffusion systems with nonlinear diffusion are investigated. system is assumed have quasi-positive nonlinearities satisfy an entropy inequality. difficulties in establishing caused by possibly degenerate overcome introducing a new class weighted truncation functions. By means the obtained solutions, we study large-time behaviour complex balanced arising from chemical reaction network theory diffusion. When does not admit boundary equilibria, shown, using method, exponentially attract same compatibility class. This extends even range diffusion, where open problem, yet able show that approximate converge uniformly regularisation parameter.