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.