37 citations · 46 across the 13 of their papers we have counts for
17 papers
A dynamic capillarity equation with stochastic forcing on manifolds: a singular limit problem
Kenneth H. Karlsen, Michael Kunzinger, Darko Mitrovic
We consider a dynamic capillarity equation with stochastic forcing on a compact Riemannian manifold . \begin{equation*}\tag{P} d \left(u_{\varepsilon,δ}-δΔ u_{\varepsilon,δ}…
Well-posedness for stochastic scalar conservation laws on Riemannian manifolds
Nikola Konatar, Darko Mitrovic, Eduard Nigsch
We consider the scalar conservation law with stochastic forcing $$ \partial_t u +\mathrm{div}_g {\mathfrak f}(\mx,u)= Φ(\mx,u) dW, \ \ {\bf x} \in M, \ \ t\geq 0 $$ on a smooth com…
A vanishing dynamic capillarity limit equation with discontinuous flux
Melanie Graf, Michael Kunzinger, Darko Mitrovic +1
We prove existence and uniqueness of a solution to the Cauchy problem corresponding to the equation \begin{equation*} \begin{cases} \partial_t u_{\varepsilon,δ} +\mathrm{div} {\mat…
Existence and Uniqueness of Singular Solutions for a Conservation Law Arising in Magnetohydrodynamics
Henrik Kalisch, Darko Mitrovic, Vincent Teyekpiti
The Brio system is a two-by-two system of conservation laws arising as a simplified model in ideal magnetohydrodynamics (MHD). The system has the form \begin{align*} \partial_t u+\…
The structure of -free measures with uniformly singular part
Darko Mitrovic
We prove that a singular part of a measure satisfying for a linear partial differential operator defined on has the range in the intersecti…
Well-posedness theory for degenerate parabolic equations on Riemannian manifolds
Melanie Graf, Michael Kunzinger, Darko Mitrovic
We consider the degenerate parabolic equation …