Renormalized Solutions for Nonlinear Parabolic Systems with Three Unbounded Nonlinearities in Weighted Sobolev Spaces

摘要

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 b1(x,u1) t div a(x, t, u1, Du1) +div Φ1(u1) + f1(x,u1,u2) = 0 in Q, b2(x,u2) t div a(x, t, u2, Du2) +div Φ2(u2) + f2(x,u1,u2) = 0 in Q, in the framework of weighted Sobolev spaces, where b(x,u) is unbounded function on u, the Carathe′odory function aisatisfying the coercivity condition, the general growth condition and only the large monotonicity, the function φiis assumed to be continuous on R and not belong to(L1 loc(Q))N.