The **well posedness** of a problem refers to whether or not the problem is stable, as determined by whether it meets the three Hadamard criteria, which tests whether or not the problem has:

**A solution:***s*exists for all*d*(for every*d*relevant to the problem).**A unique solution:***s*is unique for all d; for every data point*d*there is at most one value of*s*.**A stable solution:***s*depends continously on*d*(a tiny change in*d*will lead to a tiny change in*s*; and a large change in d will lead to a proportionally larger change in*s*).

The Hadamard criteria tells us how well a problem lends itself to mathematical analysis.

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