1. Background and examples

Problems well and badly posed

In a famous book, Hadamard introduced the notion of a well-posed problem. This is a problem whose :

• the solution exists;

• it's unique;

• it depends continuously on the data.

Of course, these notions need to be clarified by the choice of spaces (and topologies) in which the data and the solution "live".

In the same book, Hadamard suggested (and this was a widespread opinion until recently) that only a well-posed...