well-posed problem

If it is watertight, it is a well-posed problem.

The mathematical term well-posed problem stems from a definition given by Jacques Hadamard.

First, we will show that the Galerkin equation is a well-posed problem in the sense of Hadamard and therefore admits a unique solution.

Many such real-life problems are not considered to be well-posed problems mathematically, but nature provides many counterexamples of biological systems exhibiting the required function, practically.

Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions.

Indeed, some Bayesians have argued the prior state of knowledge defines the (unique) prior probability-distribution for "regular" statistical problems; cf. well-posed problems.

Inverse problems are typically ill posed, as opposed to the well-posed problems more typical when modeling physical situations where the model parameters or material properties are known.

Of the three conditions for a well-posed problem suggested by Jacques Hadamard (existence, uniqueness, stability of the solution or solutions) the condition of stability is most often violated.

He introduced the idea of well-posed problem and the method of descent in the theory of partial differential equations, culminating in his seminal book on the subject, based on lectures given at Yale University in 1922.

In his 1973 paper The Well-Posed Problem, Edwin Jaynes proposed a solution to Bertrand's paradox, based on the principle of "maximum ignorance"-that we should not use any information that is not given in the statement of the problem.

Though, it is usually possible to consider the associated abstract Cauchy problem and show that it is a well-posed problem and/or to show some qualitative properties (like preservation of positive initial data, infinite speed of propagation, convergence toward an equilibrium, smoothing properties).