9 papers
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen +1
We prove existence and uniqueness of a strong initial trace for every bounded kinetic solution of a stochastic scalar conservation law, although no initial value is prescribed and…
Multidimensional scalar conservation laws with discontinuous flux: well-posedness without non-degeneracy
Darko Mitrovic
We establish existence, uniqueness, and local \(L^1\)-stability for multidimensional scalar conservation laws with discontinuous heterogeneous flux, without imposing a non-degenera…
Orthogonality of H-distributions and applications
Nenad Antonić, Darko Mitrović, Tomislav Perić
We extend Gérard's results on orthogonality of sequences as a consequence of mutual singularity of corresponding H-measures (microlocal defect measures) to ${…
Regularity of velocity averages in kinetic equations with heterogeneity
Marko Erceg, Kenneth H. Karlsen, Darko Mitrović
This study investigates the regularity of kinetic equations with spatial heterogeneity. Recent progress has shown that velocity averages of weak solutions in () are…
On the regularity of entropy solutions to stochastic degenerate parabolic equations
Marko Erceg, Kenneth H. Karlsen, Darko Mitrović
We study the regularity of entropy solutions for quasilinear parabolic equations with anisotropic degeneracy and stochastic forcing. Building on previous works, we establish space-…
Velocity averaging under minimal conditions for deterministic and stochastic kinetic equations with irregular drift
Marko Erceg, Kenneth H. Karlsen, Darko Mitrović
This study investigates the compactness of velocity averages of sequences of solutions for a class of kinetic equations. The equations are exam…
Degenerate parabolic equations -- compactness and regularity of solutions
Marko Erceg, Darko Mitrović
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions…
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…
Velocity averaging for diffusive transport equations with discontinuous flux
Marko Erceg, Marin Mišur, Darko Mitrović
We consider a diffusive transport equation with discontinuous flux and prove the velocity averaging result under non-degeneracy conditions. In order to achieve the result, we intro…