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This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations u t − β u x x − k u x x t + γ u x x x x = f u x x . At low initial energy level ( J u 0 < d ), 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.

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