Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes in a way to ens...
Dynamic boundary conditions play an essential role in acurately modeling complex physical interactions on the boundary. In this lecture we explain the role of dynamic boundary conditions in modeling d...
Think of \begin{center} \( u_{tt} + 2au_t + Au = 0 \) \end{center} as a wave equation. Bounded solutions of this equation tend to solutions of the heat equation \begin{center} \( 2av_t + Av = 0. \) \e...
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control–to–observable inverse problems. In this context, the EnKF is known as...
In this talk we describe the influence of the initial data and the forcing terms on the regularity of the solutions to a class of evolution equations including the heat equation, linear and semilinear...
Suppose that two nonlocal minimal surfaces are included one into the other and touch at a point. Then, they must coincide. But this is perhaps less obvious than what it seems at first glance. This se...
Abstract: Let C be a Riemann surface, x_1,...,x_n a set of points on C, and a_1,...,a_n integers adding up to 0. The theorem of Abel and Jacobi determines when C carries a meromorphic function wi...
