Abstract :
In this note we show the existence of bounded solutions of the nonlinear parabolic system (u1)_t+A_1u_1=a1(x) IVu_1I^p1+f_1(x, u_1, u_2) (u2)_t+A_2u_2=a2(x) IVu_2I^p2+f_2(x, u_1, u_2) where A_i is the pseudo-Laplacian operator and ai, fi are given functions, i = 1; 2. We prove the existence of weak bounded solutions using a priori L1¡ estimate and the theory of nonlinear parabolic approximation.
