117 citations · 882 across the 65 of their papers we have counts for
10 papers · 1 filter
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}…
Galerkin-type methods for strictly parabolic equations on compact Riemannian manifolds
Melanie Graf, Michael Kunzinger, Darko Mitrovich
We prove existence of weak solutions to the Cauchy problem corresponding to various strictly parabolic equations on a compact Riemannian manifold . This also includes strict…
Laplace transformation of vector-valued distributions and applications to Cauchy-Dirichlet problems
Michael Kunzinger, Eduard A. Nigsch, Norbert Ortner
We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the…
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…
Well-posedness theory for degenerate parabolic equations on Riemannian manifolds
Melanie Graf, Michael Kunzinger, Darko Mitrovic
We consider the degenerate parabolic equation …
Wave equations on non-smooth space-times
Guenther Hoermann, Michael Kunzinger, Roland Steinbauer
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem…