Krešimir Burazin
Associate Professor

Research Interests
 Partial Differential Equations
 Continuum Physics
 Functional Analysis
Degrees

 PhD, 2008, Faculty of Natural Science, Department of Mathematics, University of Zagreb (thesis: Contributions to the theory of Friedrichs' and hyperbolic systems, in Croatian, adviser: N. Antonić)
 MSc, 2004, Faculty of Natural Science, Department of Mathematics, University of Zagreb
 BSc, 1999, Faculty of Natural Science, Department of Mathematics, University of Zagreb
 1995, Gymnasium, Vinkovci
 1991 Primary school, Komletinci
Publications
 K. Burazin, I. Crnjac, M. Vrdoljak, Optimality criteria method in 2D linearized elasticity problems, Applied Numerical Mathematics 160 (2021), 192204
 K. Burazin, I. Crnjac, Convergence of the optimality criteria method for multiple state optimal design problems, Computers & Mathematics with Applications 79/5 (2020), 13821392
 K. Burazin, J. Jankov, On the effective properties of composite elastic plate, Journal of Mathematical Analysis and Applications 495/1 (2020)
 K. Burazin, D. Mitrović, Apriori estimates for fractional diffusion equation, Optimization Letters 13/8 (2019), 17931801
 K. Burazin, M. Vrdoljak, Exact Solutions in Optimal Design Problems for Stationary Diffusion Equation, Acta Applicandae Mathematicae 161/1 (2019), 7188
 K. Burazin, J. Jankov, Smallamplitude homogenization of elastic plate equation, Applicable Analysis (2019), prihvaćen za objavljivanje
 K. Burazin, J. Jankov, M. Vrdoljak, Homogenization of elastic plate equation, Mathematical Modelling and Analysis 23/2 (2018), 190204
 K. Burazin, On Unique Solutions of MultipleState Optimal Design Problems on an Annulus, Journal of optimization theory and applications 177 (2018), 329344
 K. Burazin, I. Crnjac, M. Vrdoljak, Variant of optimality criteria method for multiple state optimal design problems, Communications in Mathematical Sciences 16/6 (2018), 15971614
 N. Antonić, K. Burazin, I. Crnjac, M. Erceg, Complex Friedrichs systems and applications, Journal of Mathematical Physics 58/10 (2017), 122
 K. Burazin, M. Erceg, Nonstationary abstract Friedrichs systems, Mediterranean Journal of Mathematics 13/6 (2016), 37773796
 K. Burazin, M. Erceg, Estimates for mild solutions to semilinear Cauchy problems, Electronic Journal of Differential Equations 2014/194 (2014), 110
 K. Burazin, M. Vrdoljak, Homogenisation theory for Friedrichs systems, Communications on Pure and Applied Analysis 13/3 (2014), 10171044
 N. Antonić, K. Burazin, M. Vrdoljak, Secondorder equations as Friedrichs systems, Nonlinear analysis: real world applications 14/1 (2014), 290305
 N. Antonić, K. Burazin, M. Vrdoljak, Heat equation as a Friedrichs system , Journal of Mathematical Analysis and Applications 404 (2013), 537553
 N. Antonić, K. Burazin, Boundary operator from matrix field formulation of boundary conditions for Friedrichs systems, Journal of Differential Equations 250 (2011), 36303651
 N. Antonić, K. Burazin, M. Vrdoljak, Connecting classical and abstract theory of Friedrichs systems via trace operator , ISRN Mathematical Analysis 2011 (2011), 114
 N. Antonić, K. Burazin, Intrinsic boundary conditions for Friedrichs systems, Communications in Partial Differential Equations 35/9 (2010), 16901715
 N. Antonić, K. Burazin, Graph spaces of firstorder linear partial differential operators, Mathematical Communications 14/1 (2009), 135156
 N. Antonić, K. Burazin, On equivalent descriptions of boundary conditions for Friedrichs systems, Mathematica Montisnigri 22 (2009), 513
 K. Burazin, Estimates on the weak solution of semilinear hyperbolic systems, Annali dell'Universita' di Ferrara 54 (2008), 229243
 N. Antonić, K. Burazin, Graph representation for asymptotic expansion in homogenisation of nonlinear firstorder equations, Annali dell'Universita' di Ferrara 53 (2007), 149176
 N. Antonić, K. Burazin, On certain properties of spaces of locally Sobolev functions, Conference on Applied Mathematics and Scientific Computing, Brijuni, 2005, 109120
 K. Burazin, U. Radojičić, Uvod u varijacijski račun i njegova povijest, Osječki matematički list 16/2 (2016), 111133U radu su prikazane osnove varijacijskog računa u slučaju kada traženi ekstrem ovisi samo o jednoj realnoj varijabli te je dan osvrt na njegov povijesni razvoj. Izvedena je EulerLagrangeova jednadžba kao nužan uvjet optimalnosti, te je pokazano da je ona i dovoljan uvjet ekstrema u slučaju konveksnog lagrangiana. Teorija je ilustrirana na povijesno važnim primjerima najkraćeg puta, geodetske krivulje na sferi, te problema brahistokrone.
 K. Burazin, J. Jankov, Glazba titrajuće žice, Osječki matematički list 14/1 (2014)
 K. Burazin, Z. Tomljanović, I. Vuksanović, Prigušivanje mehaničkih vibracija, Math.e : hrvatski matematički elektronski časopis 24 (2014)
 K. Burazin, Nelinearne diofantske jednadžbe, Osječki matematički list 7 (2007)
 K. Burazin, J. Jankov, I. Kuzmanović, I. Soldo, Primjene diferencijalnog i integralnog računa funkcija jedne varijable, Sveučilište Josipa Jurja Strossmayera u Osijeku  Odjel za matematiku, Osijek, 2017.
Projects
 Homogenization, dimension reduction and structural optimization in continuum mechanics
The project is funded by Croatian Science Foundation since 2018. Project leader: prof. Igor Velčić from University of Zagreb.
The project is funded within Interreg IPA CBC Croatia  Serbia 20142020. Partners: Institut BioSens Novi Sad (Lead Beneficiary), University of Novi Sadu  Faculty of Natural Sciences, City of Osijek, University of Osijek  Department of Mathematics. Coordinator for University of Osijek  Department of Mathematics: prof. Kristian Sabo
The project was funded by Croatian Science Foundation (July 2014  June 2018). Project leader: prof. Nenad Antonić from University of Zagreb.
 Calculus of variation, optimization and applications
This was bilateral project with Serbia (funded by Croatian Ministry of Science and Serbian Ministry of Science 2016  2017). Project leaders: N. Krejić (serbian side) and K. Burazin (croatian side)
The project is funded within programme TD COST Action TD1409. Member since 2015 as Management Committee substitut
The project was part of DAAD (German Academic Exchange Service) Programme Academic Reconstruction of South Eastern Europe which was established in late 1999, and it is funded by the German Federal Foreign Office until 2016. Eighteen universities from Germany and southeast Europe were participating in this project. Coordinators from German side were prof. Margareta Heilmann from University of Wuppertal, prof Heiner Gonska from University of DuisburgEssen and Dozent Dr. Daniela Kacsó from University of Bochum. Coordinator for University of Osijek: K. Burazin.
 Evolution Friedrichs systems
This project run in academin year 2013/14 and was funded by J.J. Strossmayer University of Osijek. Project leader: K. Burazin
Participation (as researcher) in work of following projects founded by Croatian Ministry of Science:
Titrajuća rješenja parcijalnih diferencijalnih jednadžbi (MZT 037 101)
Project run from July 2002 until June 2006 under leadership of prof. Nenad Antonić from University of Zagreb.
Titrajuća rješenja parcijalnih diferencijalnih jednadžbi (MZOS 03703727872795)
Project run from 2007 until June 2013 under leadership of prof. Nenad Antonić from University of Zagreb.
Functional analysis methods in mathematical modelling
This is bilateral project with serbia (cofinanced by Serbian Ministry of Science) that run from 2011 until 2012. Project leaders: prof. Marko Vrdoljak from University of Zagreb (croatian side) and prof. Jelena Aleksić from University of Novi Sad (serbian side).
Professional Activities
Professional Society Membership
HMD  Croatian Mathematical Society, Department Osijek
GAMM  Gesellschaft für Angewandte Mathematik und Mechanik
Refereeing/Reviewing
Editorial Boards
Invited Lectures
Primjena kompaktnosti kompenzacijom na zakone sačuvanja, Matematički kolokvij, Osijek, March 2003
On equivalence of two descriptions of boundary conditions for Friedrichs systems, The fifth international conference of applied mathematics and computing, Plovdiv, August 2008
Friedrichsovi sustavi, Matematički kolokvij, Osijek, April 2009
Friedrichsovi sustavi, Znanstveni kolokvij HMDa, Zagreb, February 2012
Nonstationary Friedrichs systems, ERCNUMERIWAVES Seminar, Basque Center for Applied Mathematics, Bilbao, November 2013
Nonstationary Friedrichs systems, Karlsruhe Institute of Technology, Karlsruhe, July, 2014
Explicit solutions of multiple state optimal design problems, Departman za matematiku i informatiku, Novi Sad, May 2016
Homogenization of KirchhoffLove plate equation and composite plates, International Workshop on PDEs: analysis and modelling, Zagreb, Croatia, June 1720, 2018
Workshops and Conferences
with talk:
Nonlocal effects in homogenisation: nonlinear firstorder equation, BosnianCroatian Analysis Meeting, Bihać, May 2001
Graphs and asymptotic expansion in homogenisation of nonlinear equations, Applied Mathematics in Changing World, Berlin, September 2001
On certain properties of spaces of locally Sobolev functions, Applied Mathematics and Scientific computing, Brijuni, June 2003
Graph representation for asymptotic expansion in homogenisation of nonlinear firstorder equations, Applied Mathematics and Scientific Computing, Brijuni, June 2005
Estimates on weak solutions of semilinear hyperbolic systems, Applied Mathematics and Scientific Computing, Brijuni, July 2007
On equivalence of two descriptions of boundary conditions for Friedrichs systems, The fifth international conference of applied mathematics and computing, Plovdiv, August 2008
Krein spaces applied to Friedrichs' systems, The Second Najman Conference on Spectral Problems for Operators and Matrices, Dubrovnik, May 2009
How to pose boundary conditions for Friedrichs systems?, Applied Mathematics and Scientific Computing, Zadar, September 2009
Boundary conditions for Friedrichs' systems,Multiscale Problems in Science and Technology. Challenges to Mathematical Analysis and Perspectives 3, Dubrovnik, June 2010
Heat equation as a Friedrichs system,Topics in PDE, Microlocal and Timefrequency Analysis, Novi Sad, September 2012
Homogenisation theory for Friedrichs systems, 8th Conference on Applied Mathematics and Scientific Computing (Dedicated to the memory of Professor Mladen Rogina), Šibenik, June 2013
Nonstationary Friedrichs systems, PDEs, Continuum Mechanics and Numerical Analysis  A Conference in Honor of the 80th Anniversary of professor Ibrahim Aganovic, Dubrovnik, May 2014
Nonstationary Friedrichs systems, ChemnitzZagreb Workshop on Harmonic Analysis for PDE, Applications, and related topics, Chemnitz, July 2014
Explicit solutions in optimal design problems for stationary diffusion equation, Partial differential equations, optimal design and numerics, Benasque, AugustSeptember 2015
Exact solutions in optimal design problems for stationary diffusion equation, The Fourth Najman Conference on Spectral Problems for Operators and Matrices, Opatija, September 2015
Exact solutions in multiple state optimal design problems, Calculus of variations and its applications (on the occasion of Luisa Mascarenhas' 65th birthday), Lisbon, December 2015
Exact solutions of multiple state optimal design problems, 6th Croatian Mathematical Congress, Zagreb, June 2016
Exact solutions of multiple state optimal design problems, International Workshop on PDEs: analysis and modelling (Celebrating 80th anniversary of professor Nedžad Limić), Zagreb, June 2016
Exact solutions of multiple state optimal design problems, Miniworkshop on PDEs: analysis and modelling, Zagreb, January 2017
Homogenization of KirchhoffLove plate equation and composite plates, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Munich, March 19  23, 2018
On composite elastic plate and HashinShtrikman bounds, VIII Partial differential equations, optimal design and numerics, Benasque, August 18  30, 2019
without talk
Phase transitions in crystalline solids, MPI–MIS Leipzig, April 2000
Second Croatian Mathematical Congress, Zagreb, June 2000
Multiscale problems in science and technology. Challenges to mathematical analysis and perspectives, Dubrovnik, September 2000
Selected issues in the mechanics of crystalline solids, Padova, October 2000
Multiscale problems in science and technology. Challenges to mathematical analysis and perspectives 2, Dubrovnik, October 2007
Forth Croatian Mathematical Congress, Osijek, June 2008
International Conference on Generalised Functions – GF2016, Dubrovnik, September 2016
Applications of Generalized Functions in Harmonic Analysis, Mechanics, Stochastics and PDE, Novi Sad, Serbia, October 25  27, 2017
International Workshop on Optimal Control of Dynamical Systems and Applications, Osijek, Croatia, June 2022, 2018
Ninth Conference on Applied Mathematics and Scientific Computing, Šibenik, Croatia, September 1720, 2018
Study Visits Abroad and Professional Improvements
Scuola Matematica Interuniversitaria, Perugia, Italy, JulyAugust 1999
Max Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany, April 2000
Carnegie Mellon University, Pittsburgh, USA, June 2001
University of Novi Sad, Novi Sad, Serbia, September 2010, AugustSeptember 2011
Bulgarian Academy of Science , Sofia, Bulgaria, October 2011, June 2012
Basque Center for Applied Mathematics, Bilbao, November 2013
BabesBolyai University, ClujNapoca, September 2014
Johann Radon Institute for Computational and Applied Mathematics, Linz, October 2014
Service Activities
Chairman of the Working seminar 2014 
Chairman of Seminar for Optimization and Applications 2017 
Vice chair for education and students at Department of Mathematics, J. J. Strossmayer University of Osijek, October 2013  September 2017
Secretary of the Mathematical Colloquium, 2003  2013
Member of the organising committee of International Workshop on PDEs: analysis and modelling (Celebrating 80th anniversary of professor Nedžad Limić), Zagreb, June 1922 2016
Member of the organising committee of International Conference on Generalised Functions – GF2016, Dubrovnik, September 49 2016
Member of the organising committee of Miniworkshop on PDEs: analysis and modelling, Zagreb, January 46 2017
Teaching
Nastavne aktivnosti u zimskom semestru Akademske 2018/2019
Funkcije više varijabli (Multidimensional Calculus)
Obične diferencijalne jednadžbe (Ordinary differential equations)
Metrički prostori (Metric spaces)
Primijenjena matematika za računalnu znanost (Applied mathematics for computer science)
Nastavne aktivnosti u ljetnom semestru Akademske 2017/2018
Kompleksna analiza (Complex analysis)
Primjene diferencijalnog i integralnog računa I (Applications of Calculus I)
Metrički prostori (Metric spaces)
Konzultacije (Office Hours): Srijeda (Wed) 11:00. Konzultacije su moguće i po dogovoru.
Teme diplomskih i završnih radova
Sljedeće teme dostupne su za diplomske i završne radove. Moguće su i druge teme prema dogovoru. Zainteresirani studenti mogu se javiti radi detaljnijih informacija.
Sustavi običnih diferencijalnih jednadžbi
Fourierovi redovi
Varijacijski račun
Banachovi i Hilbertovi prostori
L^{p} prostori (samo diplomski)
Soboljevljevi prostori (samo diplomski)
Jednadžba provođenja topline
Jednadžba stacionarnog provođenja topline
Valna jednadžba
Linearizirana elastičnost (samo diplomski)
Distribucije (samo diplomski)
Teaching experience
List of courses taught: Metric Spaces, Ordinary Differential Equations, Multivariable Calculus, Complex Analysis, Calculus 3, Calculus 4, Vector Spaces, Algebra, Elementary Mathematics 2, Differential Equations (Department of Physics), Mathematics 3, Mathematics 4 (Faculty of Civil Engineering)
Courses taught at other universities:
University of Zagreb, Faculty of Electrical Engineering and Computing: Calculus 1, Calculus 2, Calculus 3, Calculus 4, Linear Algebra
University of Bihać: Differential Geometry
College Lavoslav Ružička, Vukovar: Statistics
Postgraduate programmes: Hyperbolic and Friedrichs systems, Real and Functional Analysis, Optimal Control of Linear Dynamical Systems, Homogenization and Applications in Optimal Design
Personal
Married, two children
Member od Croatian Mountain Rescue Service
Sport interests: martial arts (Karate, Jiujitsu, Brasilian JiuJitsu), climbing, mountaineering, running, cycling, swimming.