We discuss some new well-posedness results for the continuity equation in arbitrary space dimension and we then illustrate applications to a system of conservation laws in one space dimension known as the chromatography system. In the last section, we discuss some related open problems.

To assess the quality of solutions in stochastic inverse problems, a proper measure for the distance of random variables is essential. The aim of this note is the comparison of the metrics of Ky Fan and Prokhorov with other concepts such as expected values, probability estimates and almost sure convergence. In ill-posed problems one aims to find an appropriate solution x† to an equation of the ...

Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well-posedness, we discuss positivity, L∞-contractivity and further invariance properties. We show that the parabolic problem with dynamic boundary conditions enjoy these properties if an...

This paper describes a new method for tracking of a human body in 3D motion by using constraints imposed on the body from the scene. An image-based approach for tracking exclusively uses a geometrical model of the human body. Since the model usually has a large number of degrees of freedom (DOF), a chance to be corrupted by noise increases during the tracking process, and the tracking may fall ...

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, here we show that the ill-posedness decreases when we increase the wave number.

This paper is concerned with the global well-posedness and inviscid limits of several systems of Boussinesq equations with fractional dissipation. Three main results are proven. The first result assesses the global regularity of two systems of equations close to the critical 2D Boussinesq equations. This is achieved by examining their inviscid limits. The second result relates the global regula...