Krešimir Burazin

 

Associate Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia

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phone: +385-31-224-822
fax: +385-31-224-801
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office: 19 (1st floor)

 


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

Journal Publications

  1. N. Antonić, K. Burazin, I. Crnjac, M. Erceg, Complex Friedrichs systems and applications, Journal of Mathematical Physics 58/10 (2017), 1-22
  2. K. Burazin, J. Jankov, M. Vrdoljak, Homogenization of elastic plate equation, Mathematical Modelling and Analysis (2017), prihvaćen za objavljivanje
  3. K. Burazin, M. Erceg, Non-stationary abstract Friedrichs systems, Mediterranean Journal of Mathematics 13/6 (2016), 3777-3796
  4. K. Burazin, M. Erceg, Estimates for mild solutions to semilinear Cauchy problems, Electronic Journal of Differential Equations 2014/194 (2014), 1-10
  5. K. Burazin, M. Vrdoljak, Homogenisation theory for Friedrichs systems, Communications on Pure and Applied Analysis 13/3 (2014), 1017-1044
  6. N. Antonić, K. Burazin, M. Vrdoljak, Second-order equations as Friedrichs systems, Nonlinear analysis: real world applications 14/1 (2014), 290-305
  7. N. Antonić, K. Burazin, M. Vrdoljak, Heat equation as a Friedrichs system , Journal of Mathematical Analysis and Applications 404 (2013), 537-553
  8. N. Antonić, K. Burazin, Boundary operator from matrix field formulation of boundary conditions for Friedrichs systems, Journal of Differential Equations 250 (2011), 3630-3651
  9. N. Antonić, K. Burazin, M. Vrdoljak, Connecting classical and abstract theory of Friedrichs systems via trace operator , ISRN Mathematical Analysis 2011 (2011), 1-14
  10. N. Antonić, K. Burazin, Intrinsic boundary conditions for Friedrichs systems, Communications in Partial Differential Equations 35/9 (2010), 1690-1715
  11. N. Antonić, K. Burazin, Graph spaces of first-order linear partial differential operators, Mathematical Communications 14/1 (2009), 135-156
  12. N. Antonić, K. Burazin, On equivalent descriptions of boundary conditions for Friedrichs systems, Mathematica Montisnigri 22 (2009), 5-13
  13. K. Burazin, Estimates on the weak solution of semilinear hyperbolic systems, Annali dell'Universita' di Ferrara 54 (2008), 229-243
  14. N. Antonić, K. Burazin, Graph representation for asymptotic expansion in homogenisation of nonlinear first-order equations, Annali dell'Universita' di Ferrara 53 (2007), 149-176


Refereed Proceedings

  1. N. Antonić, K. Burazin, On certain properties of spaces of locally Sobolev functions, Conference on Applied Mathematics and Scientific Computing, Brijuni, 2005, 109-120


Others

  1. K. Burazin, U. Radojičić, Uvod u varijacijski račun i njegova povijest, Osječki matematički list 16/2 (2016), 111-133
    U 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 Euler-Lagrangeova 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.
  2. K. Burazin, J. Jankov, Glazba titrajuće žice, Osječki matematički list 14/1 (2014)
  3. K. Burazin, Z. Tomljanović, I. Vuksanović, Prigušivanje mehaničkih vibracija, Math.e : hrvatski matematički elektronski časopis 24 (2014)
  4. K. Burazin, Nelinearne diofantske jednadžbe, Osječki matematički list 7 (2007)


Books

  1. 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

  • Weak convergence methods and applications

    The project is funded by Croatian Science Foundation and runs since July 2014. Project leader: prof. Nenad Antonić from University of Zagreb.

  • Calculus of variation, optimization and applications
    This is a bilateral research project with Serbia (financed by Serbian Ministry of Science and Croatian Ministry of Science) that runs since 2016. Project leaders: K. Burazin  (croatian side) and Nataša Kreić (serbian side).
  • Cost Action Mathematics for Industry Network, MI-NET, TD1409
    Member since 2015 as Management Committee substitut
  • Center of Excellence for Applications of Mathematics

    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 south-east Europe were participating in this project. Coordinators from German side were prof. Margareta Heilmann from University of Wuppertal, prof Heiner Gonska from University of Duisburg-Essen 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:

Oscilatorna rješenja parcijalnih diferencijalnih jednadžbi (MZT 037 015) 
Project run from July 1997 until June 2002 under leadership of prof. Nenad Antonić from University of Zagreb.

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 037-0372787-2795)

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

  AMS - American Mathematical Society


Refereeing/Reviewing

Mathematical Communications

Osječki matematički list


Editorial Boards

Mathematical Communications


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

Non-stationary Friedrichs systems, ERC-NUMERIWAVES Seminar, Basque Center for Applied Mathematics, Bilbao, November 2013

Non-stationary 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


Workshops and Conferences

with talk:

Nonlocal effects in homogenisation: nonlinear first-order equation, Bosnian-Croatian 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 first-order 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 Time-frequency 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

Non-stationary Friedrichs systems PDEs, Continuum Mechanics and Numerical Analysis - A Conference in Honor of the 80th Anniversary of professor Ibrahim Aganovic, Dubrovnik, May 2014

Non-stationary Friedrichs systems, Chemnitz-Zagreb 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, August-September 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

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


Study Visits Abroad and Professional Improvements

Scuola Matematica Interuniversitaria, Perugia, Italy, July-August 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, August-September 2011

Bulgarian Academy of Science , Sofia, Bulgaria, October 2011, June 2012

Basque Center for Applied Mathematics, Bilbao, November 2013

Babes-Bolyai University, Cluj-Napoca, September 2014

Johann Radon Institute for Computational and Applied Mathematics, Linz, October 2014


Service Activities

Chairman of the Working seminar 2014-

Vice chair for education and students at Department of Mathematics, J. J. Strossmayer University of Osijek, October 2013-

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)

Member of the organising  committee of International Conference on Generalised  Functions – GF2016 


Teaching

Nastavne aktivnosti u zimskom semestru Akademske 2016/2017

Funkcije više varijabli (Multidimensional Calculus)

Obične diferencijalne jednadžbe (Ordinary differential equations)

Nastavne aktivnosti u ljetnom semestru Akademske 2016/2017

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

Lp 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 (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, Homogenizacija i primjene u optimalnom dizajnu

 


Personal

Married, two children

Member od Croatian Mountain Rescue Service

Sport interests: martial arts (Karate, Jiu-jitsu, Brasilian Jiu-Jitsu), climbing, mountaineering, running, cycling, swimming.