一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性

Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy

We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.