Global solution for a system of semilinear diffusion-reaction equations with distinct diffusion coefficients

Abstract

In this paper, we show the existence of solution for a relatively general system of semilinear parabolic equations with nonlinear reaction rate terms and inflow-outflow boundary conditions. Generally, to show the existence of global solution, it has been seen in the literature that either mass conservation or some growth condition on the source term is needed. Also, in several recent works only the nonlinearity up to certain order or of certain structure is allowed. However, our work considerably weakens the ones previously made by several authors on the coefficients of the elliptic operator, on the source (reaction rate) terms as well as on the boundary conditions. Our proof is also rather small and uses an argument based on implicit function theorem.

Keywords

• semilinear parabolic equations
• system of pdes
• equilibrium reaction rates
• non-identical diffusion coefficients
• global solution
• mass action kinetics