Ill-posed problem
= Ill-posed problem
= Ill-posed
{synonym}
= Ill-posedness
{synonym}
An ill-posed problem fails existence, uniqueness or continuous dependence in the specified function spaces. Backward <heat equation> evolution is unstable because its <Fourier modes> grow like $e^{t|\xi|^2}$, making arbitrarily small high-frequency errors grow without a uniform bound.