We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under the subcritical growth restrictions on the nonlinearity f(u), which are determined by the generalized Métivier index, we establish the global existence of solutions and the corresponding attractors. Finally, we show the upper semicontinuity of the attractors in the topology of \(H_{X,0}^1(\Omega )\).

中文翻译：

---

有限简并抛物型和伪抛物型方程的适定性和长期动力学

我们考虑与 Hömander 型算子相关的简并抛物线和伪抛物线方程的初始边值问题。在由广义梅蒂维耶指数确定的非线性f ( u ) 的亚临界增长限制下，我们建立了解的全局存在性以及相应的吸引子。最后，我们展示了\(H_{X,0}^1(\Omega )\)拓扑中吸引子的上半连续性。