This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations . At low initial energy level (), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approximation and potential well methods but also obtain the finite time blow-up result by adopting the potential well and improved concavity skills. Finally, we also discussed the finite time blow-up phenomenon for certain solutions of these problems with high initial energy.

中文翻译：

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一类非线性抛物方程的初值和边值问题

本文致力于一类非线性抛物方程的初值和边值问题 。在低初始能量水平下（），我们不仅通过Galerkin逼近和势阱方法相结合证明了这些问题的整体弱解的存在，而且通过采用势阱和改进的凹度技巧获得了有限时间的爆破结果。最后，我们还讨论了具有较高初始能量的这些问题的某些解决方案的有限时间爆炸现象。