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