Renormalized Solutions for Nonlinear Parabolic Systems in the Lebesgue{Sobolev Spaces with Variable Exponents

Abstract

The existence result of renormalized solutions for a class of nonlinear parabolic systems with variable exponents. The main contribution of our work is the proof of the existence of renormalized solutions without the coercivity condition on nonlinearities which allows us to use the Gagliardo–Nirenberg theorem in the proof.Наведено результат iснування перенормованих розв’язкiв для класу нелiнiйних параболiчних систем з експонентою, що змiнюється.