We study the controllability of a coupled system linear parabolic equations, with nonnegativity constraint on state. establish two results to trajectories in large time: one for diagonal diffusion matrices an “approximate” constraint, and another stronger one, “exact” when all coefficients are equal eigenvalues coupling matrix have nonnegative real part. The proofs based “staircase” method. Fin...

Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion in bounded domain and the Neumann boundary conditions are studied case particular nonlinearities from Brusselator model, Gray-Scott Oregonator model certain predator-prey model. It is shown that considered systems have both smooth discontinuous stationary solutions, however, only ones can be stable.

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

This paper presents a quick review of reaction-diffusion systems that self-organize spatio-temporal patterns in chemical and biological systems. A pair of reaction-diffusion equations having activator and inhibitor variables is a typical model of equations describing their pattern formation processes. Some of the reaction-diffusion systems can realize several functions of image processing such ...

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 solutio...