Editing Partial differential equation (section)

=== Well-posedness ===
{{main|Well-posed problem}}
Well-posedness refers to a common schematic package of information about a PDE. To say that a PDE is well-posed, one must have:
* an existence and uniqueness theorem, asserting that by the prescription of some freely chosen functions, one can single out one specific solution of the PDE
* by [[continuity (mathematics)|continuously]] changing the free choices, one continuously changes the corresponding solution
This is, by the necessity of being applicable to several different PDE, somewhat vague. The requirement of "continuity", in particular, is ambiguous, since there are usually many inequivalent means by which it can be rigorously defined. It is, however, somewhat unusual to study a PDE without specifying a way in which it is well-posed.