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In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.  The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.  The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

在数学上，稳定性理论研究微分方程解的稳定性和动力系统在初始条件的小扰动下的轨迹的稳定性。例如，热量方程是一个稳定的偏微分方程方程，因为初始数据的微小扰动会导致随后的温度变化，这是最大值原理的结果。在偏微分方程中，人们可以使用 Lp 范数或 sup 范数来测量函数之间的距离，而在微分几何中，人们可以使用 Gromov-豪斯多夫距离来测量空间之间的距离。

在数学上，稳定性理论研究微分方程解的稳定性和动力系统在初始条件的小扰动下的轨迹的稳定性。例如，热传导方程是一个稳定的偏微分方程，因为初始数据的微小扰动会导致温度随之产生微小的变化，这是极大值原理的结果。在偏微分方程中，人们可以使用 Lp 范数或 sup 范数来度量函数之间的距离，而在微分几何中，人们可以使用 Gromov–Hausdorff 距离来度量空间之间的距离。