STUDY OF THE GLOBAL EXISTENCE OF A REACTION-DIFFUSION SYSTEM

Abstract

The goal of this work is to study the existence of solution to the following problem    @u @t − a u = − f(u, v) − u in R+ ×

@v @t − b u − d v = g(u, v) − v in R+ ×

with homogeneous Neumann boundary conditions @u @ = @v @ = 0 on R+ × @

and non-negative bounded initial data u(0, x) = u0(x) v(0, x) = v0(x) in

Where ⊂ Rn is bounded domain of class c1 ,the constants a, b, d, , and μ are positive numbers. the non-linearities f, g are assumed to be a non-negative and continuously differentiable functions on (0,+∞) × (0,+∞).