well-posed problem and ill-posed problem
well-posed problem must have the property that
- A solution exists
- The solution is unique
- The solution's behavior changes continuously with the initial conditions
简单来说就是有唯一解，并且是连续变化的。
Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions.
Problems that are not well-posed in the sense of Hadamard are termed ill-posed. Inverse problems are often ill-posed.
If the problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm. If it is not well-posed, it needs to be re-formulated for numerical treatment
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