Existence of bounded solutions for a nonlinear parabolic system with nonlinear gradient term

Abstract EN

In this note we show the existence of bounded solutions of the nonlinear parabolic system.

Ul) t + A1U1 = a1 (∝)|∇u1|p1 + f1(∝, U1, U2)) U2) t + A2U2 = a2 (∝)|∇u2|p2 + f2(∝, U1, U2)) Where At is the pseudo-Palladian operator and au U are given functions, i = 1, 2.

We prove the existence of weak bounded solutions using a priori L°°- estimate and the theory of nonlinear parabolic approximation.