Parabolic systems driven by general differential operators with variable exponents and strong nonlinearities with respect to the gradient

摘要

We consider a class of nonlinear parabolic systems driven by Leray-Lions operators with p(x)-growth conditions and strong nonlinearity with respect to the gradients. Under the assumption that a nonnegative weak super-solutions is known, we prove the existence of nonnegative weak solutions to the considered systems.