Abstract
In this article, we study the initial-boundary value problem for a p-Laplacian parabolic equation with logarithmic nonlinearity on compact metric graphs. Firstly, we apply the Galerkin approximation technique to obtain the existence of a unique local solution. Secondly, by using the potential well theory with the Nehari manifold, we establish the existence of global solutions that decay to zero at infinity for all \(p>1\), and solutions that blow up at finite time when \(p>2 \) and at infinity when \(1<p\leq 2\). Furthermore, we obtain decay estimates of the global solutions and lower bound on the blow-up rate.