AI 中文总结
该研究针对时间分数梯度流构造半凸能量与对应解，证明原能量在显式子区间严格递增，为能量单调性提供反例，完善了该领域的理论分析。
AI 中文摘要
对于时间分数梯度流，自然耗散表述通常是积分形式或经过记忆修正的形式，而非针对原能量的逐点微分不等式。我们构造了一个光滑、紧支集、全局半凸的能量，以及时间分数梯度流在有限时间区间上的绝对连续解，沿该解原能量在一个显式子区间上严格递增。该构造将初始层直接纳入轨迹，变换后曲线及其分数导数为多项式，曲线为正则浸入，海森矩阵在锚点处保持有下界。
英文摘要
For time-fractional gradient flows, natural dissipation statements are often integrated or memory-modified rather than pointwise differential inequalities for the original energy. We construct a smooth, compactly supported, globally semiconvex energy and an absolutely continuous solution on a finite time interval of a time-fractional gradient flow along which the original energy is strictly increasing on an explicit subinterval. The construction incorporates the initial layer directly into the trajectory. After transformation, the curve and its fractional derivative are polynomial, the curve is a regular immersion, and the Hessian remains bounded below up to the anchor.
