On Well Posed Generalized Best Approximation Problems

Generalized Tableaux and Formally Well-posed Initial Value Problems

We generalize the notion of a tableau of a system of partial diierential equations. This leads to an intrinsic deenition of formally well-posed initial value problems, i.e. problems with exactly the right amount of Cauchy data. We must allow here that the data is prescribed on a ag of submanifolds. The advantage of this approach is that even for non-normal systems the data can be chosen complet...

Well-posed Infinite Horizon Variational Problems

We give an effective sufficient condition for a variational problem with infinite horizon on a Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals’ flow in the cotangent bundle T ∗M ...

Quasireversibility Methods for Non-well-posed Problems

The nal value problem, ut + Au = 0 ; 0 < t < T u(T) = f with positive self-adjoint unbounded A is known to be ill-posed. One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. In this work, we will use a quasi-boundary-value method, where we perturb the nal condition to ...

Adaptive cross approximation for ill-posed problems

On Six Problems Posed