This paper deals with a pseudo-parabolic equation with variable exponents, subject to homogeneous boundary conditions with initial data in \(H_0^1(\varOmega )\). By using energy functional and Nehari functional, we classify blow-up and global existence of weak solutions in variable Sobolev spaces completely for subcritical, critical, and super critical initial energy, respectively.

中文翻译：

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变指数伪抛物线方程初能的分类

本文涉及具有可变指数的伪抛物线方程，受齐次边界条件的约束，初始数据为\(H_0^1(\varOmega )\)。通过使用能量泛函和 Nehari 泛函，我们分别针对亚临界、临界和超临界初始能量对可变 Sobolev 空间中弱解的爆炸和全局存在进行了完全分类。