A partial differential equation is ill-posed if its solution does not depend continuously on its parameters, including but not limited to boundary conditions.
Ill-Posed
See also
Ill-DefinedExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Ill-Posed." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Ill-Posed.html