On certain $L^2$-well posed mixed problems for hyperbolic system of first order

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations

L well posed Cauchy Problems and Symmetrizability of First Order Systems

A class of well-posed approximations for constrained second order hyperbolic equations

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The principle is a singular modification of the mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. The major interest of these methods is ...

Well-posedness for Hyperbolic Problems

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 ...