Explicit Invariant Regions and Global Existence of Solutions for Reaction Diffusion Systems With a Full Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions

Global existence for a strongly coupled reaction-diffusion systems with nonlinearities of exponential growth

“…On the same direction, S. Kouachi [17] has proved the global existence of solutions for two-component reaction-diffusion systems with a general full matrix of diffusion coefficients, nonhomogeneous boundary conditions and polynomial growth conditions on the nonlinear terms and he obtained in [16] the global existence of solutions for the same system with homogeneous Neumann boundary conditions and…”

Invariant Regions and Global Existence of Uniqueness Weak Solutions for Tridiagonal Reaction-Diffusion Systems

“…Usually to construct an invariant regions for systems such (1.1) we make a linear change of variables u i to obtain a new equivalent system with diagonal diffusion matrix for which standard techniques can be applied to deduce global existence (see [1,2,3,4,5,21]).…”

Generalized result on the global existence of positive solutions for a parabolic reaction diffusion model with a full diffusion matrix

“…Other techniques based mainly on invariant regions and Lyapunov functional have been developed by several authors, in some cases, allow to obtain the global existence of their reaction diffusion systems. The reader can see this technique in Kouachi's works, such as [11] and [12].…”