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The purpose of this paper is to prove the global existence in time of solutions for the coupled reaction-diffusion system:{∂  u    ∂  t    −  a  Δ  u  −  b  Δ  v  =  f     (  u  ,     v  )in     ]  0  ,     +  ∞  [  ×  Ω∂  u    ∂  t    −  c  Δ  v  =  g  (  u  ,  v  )in     ]  0  ,     +  ∞  [  ×  Ω*  *  487  *  *$$\left\{ {\matrix{{{{\partial u} \over {\partial t}} - a\Delta u - b\Delta v = f\,(u,\,v)} \hfill &amp; {{\rm in}\,]0,\, + \infty [ \times \Omega } \hfill \cr {{{\partial u} \over {\partial t}} - c\Delta v = g(u,v)} \hfill &amp; {{\rm in}\,]0,\, + \infty [ \times \Omega } \hfill } } \right.$$    with triangular matrix of diffusion coefficients.

Global solution of reaction diffusion system with non diagonal matrix