Properties of Weak Solutions for a Pseudoparabolic Equation with Logarithmic Nonlinearity of Variable Exponents

Abstract

In this paper, a new pseudoparabolic equation with logarithmic nonlinearity of variable exponents is investigated. By using the energy functional and the classical potential well, we obtain the global existence and blow-up results of weak solutions with variable exponents. These results extend and improve some recent results in which the blow-up results were showed involving the logarithmic nonlinearity with variable exponents.