Blow-Up and Global Existence of Solutions to Degenerate Kirchhoff Equation with Variable Source

In this paper, we mainly study the classification of global existence and blow-up of solutions to degenerate Kirchhoff problems for the initial energy at different conditions. Firstly, under subcritical or critical conditions, we find two invariant sets and obtain the threshold results of global existence or blow-up in finite time. Furthermore, we apply \(\omega \) $\omega$ -limit to prove the existence of blow-up solutions for the supercritical initial energy case. Finally, we give two-sided estimates of asymptotic behavior when the source term is controlled by the diffusion term.