Existence of solutions to a strongly nonlinear parabolic-elliptic coupled system of infinite order

In this paper, we are concerned with the problem of existence of a capacity solution to the strongly nonlinear degenerate problem, namely, partial derivative theta/partial derivative t+H(theta) = sigma(theta)vertical bar del phi vertical bar(2), div(sigma(theta)del phi) = 0 in Q, where the operator H is of the form H(theta) = Sigma(infinity)(vertical bar nu vertical bar=0) (-1)(vertical bar nu vertical bar) D-nu(H-nu(t, x, D-gamma theta)), vertical bar gamma vertical bar <= vertical bar nu vertical bar. By using a Schauder's fixed point theorem, we establish the existence of weak solutions to a certain truncated problem of finite order. Then, we demonstrate that the sequence of solutions to this truncated problem converges (up to a subsequence) to a capacity solution to our problem of infinite order.