Kirchhoff-Pohozaev波动方程解的存在性与等度连续性
Existence and equicontinuity of solutions to the Kirchhoff--Pohozaev wave equation
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中文总结 AI 辅助
针对Boiti-Manfrin发现的具有无穷多守恒量的Kirchhoff-Pohozaev波动方程变体，本文推导守恒量显式公式与强制性生成函数，建立先验界、等度连续性传播及整体适定性，证明整体C_t H^1解存在。
中文摘要 AI 辅助
Boiti-Manfrin近期发现，由Pohozaev提出的Kirchhoff波动方程的变体具有无穷多个守恒量。本文中，我们得到了这类守恒量的显式公式，还引入了一个对这些守恒量具有强制性的生成函数。随后利用这些工具建立了先验界、等度连续性的传播、s≥3/2时在H^s空间中的整体适定性，以及整体C_t H^1解的存在性。
英文摘要
It was recently discovered by Boiti--Manfrin that a variant of the Kirchhoff wave equation introduced by Pohozaev admits infinitely many conserved quantities. In this paper, we obtain explicit formulae for such conserved quantities, as well as introduce a generating function for them that is coercive. These tools are then employed to establish a priori bounds, the propagation of equicontinuity, global well-posedness in $\mathcal H^s$ for $s\geq \frac32$, and the existence of global $C_t \mathcal H^1$ solutions.
