Hadamard and "well-posed" problems. I can't really find much clarification on Hadamard's definition of a well-posed problem. My confusion comes from knowing exactly what is meant by the second and third properties: 2) The solution is unique 3) The solution depends continuously on the data, in some reasonable topology. http://en.wikipedia.org/wiki/Well-posed_problem" [Broken] For example, a solution would exist for a PDE y * uxx = x * uyy with u(0,y) = 2 and u(x,0) = 2 that is simply a constant. But is the solution, u=2, considered unique? Does the solution depend on the data? Does the solution for u(x,y) fail property 3 because it no longer satisfies the PDE if the initial conditions are changed? Edit: Maybe this belongs in the Differential Equations forum. Sorry. Can this be moved? Thanks.