 Well-posed problem

A problem is well posed in the sense of Hadamard when a solution exists for every admissible datum, is unique, and depends continuously on the data. Failure of any condition makes it ill posed.

A well-posed problem is a concept from mathematics, particularly in the context of mathematical analysis and the theory of partial differential equations. The term is typically attributed to the French mathematician Jacques Hadamard, who outlined specific criteria for a problem to be considered well-posed. According to Hadamard, a problem is well-posed if it satisfies the following three conditions: 1. **Existence**: There is at least one solution to the problem.