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Martin Lazar 

Field of research

         Control theory: Control of parameter dependent systems (greedy control, averaged control),
                                      optimal control of parabolic problems
         Microlocal analysis: PDEs and homogenisation, velocity averaging,
                                                    microlocal defect functionals (1-scale H-measures, semiclassical measures, H-distributions)
         Geophysical fluid dynamics: analytical modelling in oceanography  
       

Top 5 publications

Stability of Observations of Partial Differential Equations under Uncertain Perturbations,

ESAIM:COCV, in press

Greedy controllability of finite dimensional linear systems,

Automatica 74 (2016) 327–340, with E. Zuazua

Parabolic H-measures,
J. Funct. Anal. 265 (2013), 1190--1239, with N. Antonić

  Velocity averaging – a general framework,

Dynamics of PDE 9 (2012), 239—260, with D. Mitrović

Cyclonic vs. anticyclonic circulation in lakes and inland seas,

Journal of Physical Oceanography 39 (2009), 2247 – 2263, with M. Orlić

Affiliations

2008 - present        University of Dubrovnik, Croatia
2015 (May - July)    Basque Center for Applied Mathematics, Bilbao, Spain
2013 (Mar - Sep)    Basque Center for Applied Mathematics, Bilbao, Spain
1998 - 2008            Department of Mathematics, University of Zagreb, Croatia
1999 - 2000            Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany

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Education     

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Publications
(the complete list on http://bib.irb.hr/lista-radova?autor=251633):

SUBMITTED:

Optimal distributed control of the heat-type equations by spectral decomposition,

submitted, 40 pp, with C. Molinari

Stability of Observations of Partial Differential Equations under Uncertain Perturbations,

ESAIM:COCV, 17 pp, in press

Characteristic scales of bounded L2 sequences ,

submitted, 18 pp, with M. Erceg

PUBLISHED:

Optimal control of parabolic equations by spectral decomposition,

Optimization, 66(8) (2017) 1359—1381, with C. Molinari and J. Peypouquet

Localisation principle for one-scale H-measures,

J. Funct. Anal., 272 (2017) 3410–3454, with N. Antonić and M. Erceg

On a new class of functional spaces with application to the velocity averaging,
Glas. Mat. Ser. III, 52 (2017) 115-130, with D. Mitrović

Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation,
Appl. Anal, 96(16) (2017) 2832-2845

Existence of solutions for a scalar conservation law with a flux of low regularity,
Electron. J. Diff. Equ. 2016 (2016) 1–18, with D. Mitrović

Greedy controllability of finite dimensional linear systems,

Automatica 74 (2016) 327–340, with E. Zuazua

Averaged control and observation of parameter-depending wave equations,

C. R. Acad. Sci. Paris, Ser. I 352 (2014) 497--502, with E. Zuazua
On the velocity averaging for equations with optimal heterogeneous rough coefficients,

arXiv:1310.4285, preprint, 2013, with D. Mitrović

Parabolic H-measures,
J. Funct. Anal. 265 (2013), 1190--1239, with N. Antonić

On an extension of a bilinear functional on  $L^p(R^d) \\times E$ to a   Bochner space with an application to velocity averaging, 

         C. R. Acad. Sci. Paris Ser. I Math,  351 (2013), 261--264, with D. Mitrović

Velocity averaging – a general framework,
Dynamics of PDE 9 (2012), 239—260, with D. Mitrović

The velocity averaging for a heterogeneous heat type equation,

Math. Comun. 16 (2011), 271– 282, with D. Mitrović

Parabolic variant of H-measures in homogenisation of a model problem based on Navier-Stokes equation,

Nonlinear analysis - Real world application 11 (2010), 4500 – 4512, with N. Antonić

Cyclonic vs. anticyclonic circulation in lakes and inland seas,

Journal of Physical Oceanography 39 (2009), 2247 – 2263, with M. Orlić

A parabolic variant of H-measures,

Annali Universita' di Ferrara 54 (2008), 183 – 201, with N. Antonić

H-measures and variants applied to parabolic equations,

J. Math. Anal. Appl 343 (2008), 207 – 225, with N. Antonić

An application of parabolic variant of H-measures,

Proc. Appl. Math. Mech 7 (2007), 2040023-2040024, with N. Antonić

Analytical Modelling of Wintertme Coastal Jets in the Adriatic Sea,

Continental Shelf Research 27 (2007) 275 – 285, with M. Pavic, Z. Pasaric and M. Orlic

Microlocal energy density for hyperbolic systems,

Proceedings of the Second Conference on Applied Mathematics and Computation,Z. Drmac et al., eds., Kluwer Academic/Plenum Publishers (2003) 179 – 190 with N. Antonić
Computation of Power-Series Expansions in Homogenisation of Nonlinear Equations,

Proceedings of the 1. Conference on Applied Mathematics and Computation, M. Rogina et al., eds., Department of Mathematics, Zagreb, (2001) 69 – 80, with N. Antonić

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Projects

Leader of international projects

Transport in highly heterogeneous media
(Croatian – Montenegrin bilateral project, 2013 – 2014)
The project task is a study of generalised transport equations for a wide class of functions and coefficients describing the processes, in such a way describing more realistic phenomena. The main mathematical tool used in the study are H-measures and their variants.

Leader of national projects

Greedy control
(University of Dubrovnik, 2015)
Analytical Modelling of thermohaline circulation in land-locked basins with vertically variable density
(University of Dubrovnik, 2014)

Collaborator in international projects

The cost of controlling the heat flow in a multiscale setting,
Leader: I. Nakić (Croatian – German bilateral project, 2016 – 2017)
Partial Differential Equations: Analysis, Control, Numerics and Applications,
Leader: E. Zuazua (MTM2011-29306, Spanish Ministry of Economy and Competitiveness, May – July 2015)
Multiscale methods and calculus of variations,
Leader: N. Antonić (Croatian – Montenegrin bilateral project, 2015 – 2016)
NUMERIWAVES, New analytical and numerical methods in wave propagation,
Leader: E. Zuazua (European Research Council project, March – September 2013)
Meduza: Collaborative International Research on Gelatinous Zooplankton,
Leader: A. Benović (American – Croatian – Italian – Slovenian project, 2003)

Collaborator in national projects

Weak Convergence Methods and Apllications,
Leader: Nenad Antonić (Croatian Science Foundation, 2014 –)
Oscillatory Solutions of Partial Differential Equations,
Leader: Nenad Antonić (Croatian Ministry of Science, Education and Sports, 1998 – 2002, 2002 – 2006, 2007 – 2013)
Mathematical Modelling of Geophysical Phenomena,
Leader: Marko Vrdoljak (Croatian Ministry of Science, Education and Sports, 2009 – 2013)

Coordinator:

DAAD: Centre of Excellence for Applications of Mathematics,
(for University of Dubrovnik, 2010-today).

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Dissemination

Invited lectures:

  Greedy control,

International Conference of the Euro-Maghreb Laboratory of Mathematics and their Interactions, Hammamet, Tunisia, April 27 – Mai 1, 2016.

  Stability of Observations of Partial Differential Equations under Uncertain Perturbations,

New trends in modeling, control and inverse problems, Toulouse, France, June 16 – 19, 2014.

  Generalised Functions - Distributions,

DAAD School on Homogenisation, multi-scale methods and applications, Dubrovnik, Croatia, May 31 – June 4, 2010.

  H-measures, variants and applications,,

DAAD School on Measure Theoretical Tools in Partial Differential Equations, Budva, Montenegro, October 4 – 10, 2009.

Conference talks:

  Exploring Limit Behaviour of Non-quadratic Terms via H-measures. Application to Small Amplitude Homogenisation,

International Conference on Generalized Functions GF2016, Dubrovnik, Croatia, September 4 – 9, 2016.

  Greedy control,

7th European Congress of Mathematics, Berlin, Germany, July 18 – 22, 2016.

  Stability of Observations of Partial Differential Equations under Uncertain Perturbations,

International Workshop on PDEs: analysis and modelling, Zagreb, Croatia, June 19 – 22, 2016.

  Greedy control,

6th Croatian Mathematical Congress, Zagreb, Croatia, June 14 – 17, 2016.

  Greedy control,

Controllability of Partial Differential Equations and Applications, Marseille, France, November 9 – 13, 2015.

  Greedy control,

The 4th Najman conference on spectral problems for operators and matrices,Opatija, Croatia, September 20 – 25, 2015.

  Greedy control,

Partial differential equations, optimal design and numerics, Benasque, Spain, August 23 – September 4, 2015.

  Stability of Observations of Partial Differential Equations under Uncertain Perturbations,

PDEs, Continuum Mechanics and Numerical Analysis, Dubrovnik, Croatia, May 26 – 30, 2014.
  Averaged observability,
Partial Differential Equations, Optimal Design and Numerics, Benasque, Spain,   Aug 25 - Sep 5, 2013.
Velocity averaging - a general framework,

Topis in PDE, Microlocal and Time-frequency Analysis, Novi Sad, Serbia, September 3 – 8, 2012

Application of parabolic H-measures to the vibrating plate equation,

Seventh Conference on Applied Mathematics and Scientific Computing, ApplMath11, Trogir, Croatia, June 13 – 17, 2011

  The velocity averaging for an ultra-parabolic heterogeneous equation,

Multiscale problems in Science and Tehcnology 3, Dubrovnik, Croatia, May 31 – June 4, 2010

The velocity averaging for a heat type equation,

Sixth Conference on Applied Mathematics and Scientific Computing, Zadar, Croatia, September 14 – 18, 2009

What supports occasional anticyclonic bottom flow in the Adriatic?
Recent Advances in Adriatic Oceanography and Marine Meteorology, Dubrovnik, Croatia, November 5 – 7, 2008

What feeds oscillations in the Schroedinger type equations?
Scaling Up and Modeling for Transport and Flow in Porous Media, Dubrovnik, Croatia, October 13 – 16, 2008

On transport property of variant H-measures,
Multiscale problems in Science and Tehcnology 2, Dubrovnik, Croatia, October 1 – 6, 2007

Variant H-measures and applications,
6th International Congress on Industrial and Applied Mathematics, Zurich, Switzerland, July 16 – 20, 2007

A Parabolic Variant of H-measures,         
Conference on Applied Analysis, Carnegie-Mellon University, Pittsburgh, USA, October 19 – 21, 2006

H-measures applied to Parabolic Equations,
Frontiers of  Applied Analysis, Carnegie-Mellon University, Pittsburgh, USA, September 8 – 10, 2005

H-measures applied to Nonhyperbolic Equations,
Fourth Conference on Applied Mathematics and Scientific Computing, Brijuni, Croatia, June 19 – 24, 2005

Analytic modelling of thermohaline circulation and quasigeostrophic flow in the Adriatic sea,
School and Workshop on Oceanography, Lakes and Rivers, Instituto Superior Tecnico, Lisbon, Portugal, July 19 – 24, 2004

Microlocal energy density for hyperbolic systems,
Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, June 4 – 9, 2001

Microlocal energy density for semilinear wave equations,
Bosnian Croatian Analysis Meeting, Bihac, Bosnia and Herzegovina, May 10 – 12, 2001

Computation of power-series expansions in homogenisation of nonlinear equations,
Applied Mathematics and Computation, Dubrovnik, Croatia, September 13 – 18, 1999                                                      

Posters:

Modelling of bottom anticyclonic circulation in the Adriatic Sea,
Medcoast 05, The Seventh International Conference on the Mediterranean Coastal Environment, Kusadasi, Turkey, October, 25 – 29, 2005.

Cyclonic vs. anticyclonic circulation in the Adriatic Sea,
European Geosciences, General assembly 2005, Vienna, Austria, April 24 – 29, 2005.

Analytic modelling of thermohaline circulation and quasigeostrophic flow in the Adriatic Sea,
Prvi kongres hrvatskih znanstvenika iz domovine i inozemstva, Zagreb - Vukovar, Croatia, November 15-19, 2004.

Analytic modelling of thermohaline circulation and quasigeostrophic flow in the Adriatic Sea,
1st General Assembly of European Geosciences Union,  Nice, France, April 25 – 30, 2004.

Analiticko modeliranje termohaline cirkulacije i kvazigeostrofickog strujanja u sjevernom Jadranu,
4. znanstveni sastanak hrvatskog fizikalnog drustva, Zagreb, Croatia, November 13 – 15, 2003.

Other attended schools and conferences: 

Geophysical and Environmental Fluid Dynamics Summer School, (University of Cambridge, Cambridge,
UK, September 11-24, 2005)

2004 CNA Summer School: Advances in Nonlinear Analysis, (Carnegie-Mellon University, Pittsburgh, USA, May 27 – June 5, 2004)

Summer school in Mathematics - CIMPA-UNESCO and CEU, (Budapest, Hungary, September 8 – 21, 2002)

Multiscale Problems in Science and Technology, (Dubrovnik, Croatia, September 3 – 9, 2000)

Phase Transitions in Crystalline Solids, (Leipzig, Germany, April 28 – 30, 2000.)

Scuola Matematica Interuniversitaria, (Perugia, Italia, July 26 – August 28, 1998)

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Expeditions

    Meduza II:  Collaborative international research on gelatinous zooplankton of the Adriatic Sea,
    Island of Mljet, Croatia, July 1-30, 2003.

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Teaching experience

UNDERGRADUATE AND GRADUATE PROGRAMS
University of Dubrovnik

AQUACULTURE: Applied mathematics and biometry (2002 – );
APPLIED/BUSINESS COMPUTING: Mathematical Analysis I, II (2008 – ), Statistics and Probability (2008 – );
ELECTRICAL ENGINEERING AND COMMUNICATION TECHNOLOGIES: Mathematics IV (2008 – ).

University of Zagreb

MATHEMATICS: Partial Differential Equations (2004 – 2008), Linear Algebra I, II (2003 – 2008), Mathematical Analysis I, II (2000 – 2002), Hyperbolic Systems (2002);
PHYSICS: Mathematical Analysis in Space (2007), Mathematical Analysis I, II (1998 – 1999);
CHEMISTRY: Mathematics I, II (1998 – 1999).

American College for Management and Technology in Dubrovnik

MANAGEMENT: Statistics III (2009 – ), Statistics I (2002 – 2004).

POSTGRADUATE PROGRAMS
University of Zagreb

Mathematics: Pseudodifferential Operators (2008/09).

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 Honours/Fellowships

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Skills and Competencies

Language proficiency

speaking                   Croatian (native), English, German, Spanish
communicating         Hungarian
reading                      Latin

Computer skills

UNIX, PC                  at the regular user level
applications            Metapost, TeX, Emacs, Excel, Minitab, Mapple, Matlab
programming          C, Pascal, Fortran

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Personal information

Place of birth:            Dubrovnik, Croatia
Date of birth:             April 4, 1975
Children:                    Jakov (2006), Stjepan Domagoj (2011), Lukrecija (2014)

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Copyright ©2014, ML

Cretaed: April 2014. Last edit: November 2015.