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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 (1scale
Hmeasures, semiclassical measures, Hdistributions)
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
Hmeasures,
J. Funct. Anal. 265 (2013),
11901239, 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
MaxPlanck Institute
for Mathematics in the Sciences, Leipzig, Germany
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Education
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SUBMITTED:

Optimal
distributed control of the heattype 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 onescale Hmeasures,

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)
115130, with D. Mitrović

Exploring
limit behaviour of nonquadratic terms via Hmeasures.
Application to small amplitude homogenisation,
Appl. Anal, 96(16)
(2017)
28322845

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 parameterdepending wave equations,

C.
R. Acad. Sci. Paris, Ser. I 352
(2014)
497502, with E. Zuazua
On
the velocity averaging for equations with optimal heterogeneous
rough coefficients,

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

Parabolic
Hmeasures,
J.
Funct. Anal. 265
(2013),
11901239, 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),
261264, 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 Hmeasures in homogenisation of a model problem based
on NavierStokes 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 Hmeasures,

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

Hmeasures
and variants applied to parabolic equations,

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

An
application of parabolic variant
of Hmeasures,

Proc. Appl. Math. Mech 7
(2007),
20400232040024, 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 PowerSeries 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 Hmeasures and their variants.
Leader of national projects
Greedy control (University of Dubrovnik, 2015)
Analytical Modelling of thermohaline circulation in landlocked
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 (MTM201129306,
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, 2010today).
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Dissemination
Invited lectures:

Greedy control,

International
Conference of the EuroMaghreb 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, multiscale methods and applications,
Dubrovnik, Croatia, May 31 – June 4, 2010.

Hmeasures, 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 Nonquadratic Terms via
Hmeasures. 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 Timefrequency Analysis, Novi Sad, Serbia,
September 3 – 8, 2012

Application of parabolic Hmeasures 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 ultraparabolic 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 Hmeasures,
Multiscale
problems in Science and Tehcnology 2, Dubrovnik, Croatia,
October 1 – 6, 2007

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

A Parabolic Variant of Hmeasures,
Conference
on Applied Analysis, CarnegieMellon University, Pittsburgh,
USA, October 19 – 21, 2006

Hmeasures applied to Parabolic Equations,
Frontiers
of Applied Analysis, CarnegieMellon University,
Pittsburgh, USA, September 8 – 10, 2005

Hmeasures 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 powerseries 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 1519, 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 1124, 2005)

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

Summer
school in Mathematics  CIMPAUNESCO 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
130, 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
2013

Basque
Center for Applied Mathematics, Bilbao, Spain, Postdoctoral
Fellow
(invited to take part on
problems concerning Hmeasures and their applications within
the NUMERIWAVES
project, leader: E. Zuazua)

2007

Radon Institute for Computational and Applied Mathematics,
Linz, Austria (invited to a twoweek stay with an
idea of launching common projects)

2005

TEMPUS Individual Mobility Grant (for the two
weeks Attendace of the Geophysical and Enviromental Fluid
Dynamics Summer School, University of Cambridge)

19992000

Max Planck Institute for
Mathematics in the Sciences in Leipzig, Germany
(invited to take part on projects concerning Hmeasures and
their applications under leadership of S. Müller)

1997

Scholarship of the University of Zagreb (70 such
scholarships for 40 000 students)

1989

Second prize at the Croatian Competition in Mathematics,
Zadar, Croatia

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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.
