(untitled) (Analysis in Theory and Applications, 2013)
We prove an existence result without assumptions on the growth of some nonlinear terms, and the existence of a renormalized solution. In this work, we study the existence of renormalized solutions for a class of nonlinear parabolic systems with three unbounded nonlinearities, in the form {arrayll b_1(x,u_1)t- div(a(x,t,u_1,Du_1))+div(Φ_1(u_1))+ f_1(x,u_1,u_2)= 0 & in Q, b_2(x,u_2)t- div(a(x,t,u_2,Du_2))+div(Φ_2(u_2))+ f_2(x,u_1,u_2)= 0 & in Q, array.in the framework of weighted Sobolev spaces, where b(x,u) is unbounded function on u, the Carathéodory function a_i satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function φ_i is assumed to be continuous on R and not belong to (L^1_loc(Q))^N.