Existence and blow-up of weak solutions of a pseudo-parabolic equation with logarithmic nonlinearity

Abstract

Abstract In this paper, we prove the existence of weak solutions of a pseudo-parabolic equation with logarithmic nonlinearity in an interval [ 0 , T ) $[0, T)$ by employing the Galerkin approximation method and compactness arguments. We show that the solutions become unbounded at a finite time T ⋆ $T^{\star}$ and find upper and lower bounds for this time.

Keywords

• Weak solutions
• Blow-up
• Variable exponent spaces
• Galerkin method
• p ( x ) $p(x)$ -Laplacian operator