Remarks on a (p(x), q(x))-Laplacian Parabolic System with Logarithmic Nonlinearity

Abstract

In this work, we investigate a system of (p(x),q(x))-Laplacian parabolic equations with logarithmic nonlinearity. Some results on the blow-up and asymptotic behavior of weak solutions are derived by using potential well theory combined with the Nehari manifold. The main difficulties here come from the lack of homogeneous properties on the variable exponent spaces and the sign-changing of reaction terms. Our results improve a recent result obtained in [3].