Darko Mitrovic

Office: A302 (3rd floor)
email address: darko.mitrovic [at] math.hr

Address:
Prirodnoslovno-matematicki fakultet
Bijenicka cesta 32
10 000 Zagreb
Croatia

Faculty of Mathematics
University of Montenegro
Cetinjski put bb
Podgorica, Montenegro

Research interests

partial differential equations and calculus of variations; hyperbolic conservation laws; analysis and numerics of transport in the highly heterogeneous media

Education

PhD in Mathematics: Partial Differential Equations, thesis: Formation and Interaction of Singularities for Scalar Conservation Laws with Convex Nonlinearities, October 2005, University of Montenegro (advisor: V.G.Danilov, Moscow Institute for Electronics and Mathematics, Moscow, Russia)
MSc in Mathematics: Linear and Quasi-linear Elliptic Partial Differential Equations and Their Generalized Solutions, December 2001, University of Novi Sad
BSc in Mathematics: Theoretical Mathematics, July 1999, University of Montenegro

Work experience

December 2014 - December 2015 (planned): visiting professor at University of Zagreb within the frame of the FP7 Marie Curie FP7-PEOPLE-2011-COFUND project Micro-local defect functionals and applications (MiLDeFA)
February 2001- today: Department of Mathematics, University of Montenegro; Position: Associate professor (from March 2012 - today), Assistant professor (October 2006 - March 2012), teaching assistant (February 2001 - October 2006)
October 2006 - October 2007: postdoc at Norwegian University For Technical Sciences, Trondheim, Norway
March 2010 - September 2013: 20% research position at the University of Bergen, Bergen, Norway

CV

You can find my short CV here.

Publications

The most relevant publications in the last 7 years (full list can be found at: http://scholar.google.com/citations?user=B6wOodYAAAAJ&hl=en):

Misur, M; Mitrovic, D.: On a Generalization of Compensated Compactness in the L^p-L^q setting, Journal of Functional Analysis 268 (2015) 1904-1927
Antonic, N.; Misur, M.; Mitrovic, D.: On the First Commutation Lemma, in preparation
Andreianov, B.; Mitrovic, D.: Entropy conditions for scalar conservation laws with discontinuous flux revisited, Annales Institut Henri Poincare C - Analyse Non Lineaire, 29 pages, in print
Kalisch, H.; Mitrović, D.; Nordbotten, J. M.: Rayleigh-Taylor instability of immiscible fluids in porous media, Continuum Mechanics and Thermodynamics, 13 pages, in print
Kalisch, H.; Mitrović, D.; Nordbotten, J. M.: Non-standard Shocks in the Buckley-Leverett Equation, Journal of Mathematical Analysis and Applications, accepted for publication
Mitrović, D.; Novak, A.: Two phase nonturbulent flow with applications, Mathematical Problems in Engineering, Volume 2015 (2015), Article ID 439704, 8 pages
Aleksić, J.; Mitrović, D.: Strong traces for averaged solutions of heterogeneous ultra-parabolic transport equations, to appear in J. of Hyperbolic Differential Equations.
Lazar, M; Mitrović, D.: On an extension of a bilinear functional on Lp(Rd)⊗E to a Bochner space with an application on velocity averaging, C. R. Acad. Sci. Paris Ser. I Math. 351 (2013), 261-- 264.
Lazar, M.; Mitrović, D.: Velocity averaging general framework, Dynamics of Partial Differential Equations, Vol.9, No.3, 239-260, 2012.
Kalisch, H.; Mitrović, D.: Singular solutions of a fully nonlinear 2x2 system of conservation laws, Proceedings of the Edinburgh Mathematical Society, 55 (2012), 711-729.
Antonić, N.; Mitrović, D.: H-distributions An extension of the H-distributions in the Lp-Lq setting, Abstr. Appl. Analysis, 2011 (2011), Article ID 901084, 12 pages, doi:10.1155/2011/901084
Mitrović, D.; Ivec, I.: A Generalization of H-measures and Application on Purely Fractional Scalar Conservation Laws, Communication on Pure and Applied Analysis, Vol. 10, No. 6 (2011), 1617 – 1627.
Mitrović, D.: New Entropy Conditions for Scalar Conservation Laws with Discontinuous Flux, Discrete and Continuous Dynamical Systems-A, Vol. 30 (2011) (20 pages, 4 figures)
Aleksić, J.; Mitrović, D.: On the compactness for two dimensional scalar conservation laws with discontinuous flux, Communications in Mathematical Sciences, Vol. 7 (2009), 963-971.
Aleksić, J.; Mitrović, D.; Pilipović, S.: Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media, Journal of Evolution Equations, Vol. 9 (2009), 809-828.
Danilov, V. G.; Mitrović, D.: Delta shock wave formation in the case of triangular hyperbolic system of conservation laws, Journal of Differential Equations, 245(2008) 3704-3734

Research projects

Project leader of the project Advection diffusion equations in heterogeneous media funded by Ministry of Sciences of Montenegro. Duration 2012-2014
DAAD: Centre of Excellence for Applications of Mathematics (coordinator for University of Montenegro, 2009-today)
Project leader of the bilateral project Transport in Highly Heterogeneous Media funded by Ministry of Sciences, Education and Sport of Croatia and Ministry of Sciences of Montenegro. Duration 2013-2014
HRZZ: Weak convergence methods and applications (collaborator; 2014-2018, leader: Nenad Antonić)
FP7 project Micro-local defect functional and applications (MiLDeFA) in the frame of the program Marie Curie FP7-PEOPLE-2011-COFUND

Skills and competencies

languages:	south slavic languages (native)
	russian (fluent)
	english (fluent)
	norwegian (professional)
	french (professional)
computer skills:	Matlab, Latex, Tex; familiar with Linux (Ubuntu); Windows XP office

Teaching (at University of Zagreb)

During the academic year 2014-2015, together with prof. Nenad Antonic, I am giving doctoral lectures on Microlocal defect functionals.

External links

Last update: March 2015