(adsbygoogle = window.adsbygoogle || []).push({}); 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 * u_{xx}= x * u_{yy}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.

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# Hadamard and well-posed problems.

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