Coarsening in high order, discrete, ill-posed diffusion equations

Refined Upper Bounds on the Coarsening Rate of Discrete, Ill-posed Diffusion Equations

We study coarsening phenomena observed in discrete, ill-posed diffusion equations that arise in a variety of applications, including computer vision, population dynamics, and granular flow. Our results provide rigorous upper bounds on the coarsening rate in any dimension. Heuristic arguments and numerical experiments we perform indicate that the bounds are in agreement with the actual rate of c...

FGMRES for linear discrete ill-posed problems

GMRES is one of the most popular iterative methods for the solution of large linear systems of equations. However, GMRES generally does not perform well when applied to the solution of linear systems of equations that arise from the discretization of linear ill-posed problems with error-contaminated data represented by the right-hand side. Such linear systems are commonly referred to as linear ...

Approximation of Ill-posed Boussinesq Equations

In this paper we study finite dimensional approximations to Boussinesq type equations. Our methods are based on infinite dimensional center manifold theory. The main advantage of our approach is that we can handle both well-posed and ill-posed versions of the Boussinesq equation. We show that for suitable initial conditions, our approximations describe the dynamics accurately for long enough ti...

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

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