Existence and blow up of solutions for a singular higher-order viscoelastic parabolic equation with logarithmic nonlinearity

Abstract

In this work, we obtain the singular higher-order viscoelastic parabolic type equation with logarithmic nonlinearity. We establish the local existence, global existence and blow up of solutions. By employing the cut-off technique and the Faedo-Galerkin approximation method, the local existence of a weak solution is established. The global existence of the weak solution is then derived using the potential well method. Moreover, we demonstrate that the blow up in finite time through the application of concavity method.