**Department of Differential Equations and Mathematical Physics**

### Short history of the department

Department of Differential Equations and Mathematical Physics at IMI - BAS was established in 2011 as an unification of the Department of Differential Equations and Department of Mathematical Physics and its head now is Prof. Angela Slavova.Department of Differential equations was founded in 1967 and its first leader was Prof. G. Bradistilov (1967-1971). In 1987 a Mathematical Physics Laboratory was founded (Department of Mathematical Physics of IMI BAS) based on the Department of Differential Equations. The first head was Prof. Marin Marinov.

Members of the section have participated in hundreds of scientific conferences in Bulgaria and abroad. Almost all members of the Department have been invited to give lectures in prestigious European (UK, Germany, France, Italy, Belgium, Netherlands, Spain, etc.), American (U.S., Canada, Australia) universities, and also in China, Japan, etc.

Members of the department have had a number of M.Sc. and Ph.D. students. More than 11 Ph.D. students have had advisors form the department of DE at IMI - BAS. In the department were included the following Ph.D. students: K,Janakiev, N.Tzvetkov (who is at regular work in CNRS, Orsay, Paris now), Borislav Yordanov (who is now working at Hokkaido University, Japan), Rumjana Kirova, K.Azgorov, G. Venkov, A.Ivanov, Ljubomira Softova, Maya Markova, Yonko Stoynov, Viktoria Rashkova.

Since 2014 Department of Differential Equations and Mathematical Physics is organizing International Conference “New Trends of the Applications of Differential Equations in Sciences” (NTADES): **www.math.bas.bg/ntades**

### Main fields of scientific research in the department are:

- PDEs describing arising, propagation and interaction of nonlinear waves, as for example tidal waves in ocean, tsunami waves, shallow water waves, etc. This field is included in the priority climate changes and environmental security of the National strategy for scientific investigations 2020 and environment of the Horizon 2020;
- Financial mathematical problems for risk management – Black- Scholes equation, Heston equation via CNN method – theoretical and numerical. This field has expected economical effect on the financial markets, as well as risk management;
- Boundary integral equation method for obtaining numerical results for the propagation of waves in inhomogeneous areas with discontinuities having applications in seismic mechanics and mechanics of distructions. This field is connected with security and society priority of Horizon 2020.
- Dissipative wave equations with applications in biology. Klein Gordon models in DNA and protein molecules. This field is in the frames of priority applications in biology of Horizon 2020 and priority health and quality of life of the National strategy of scientific investigations 2020;
- New methods for integration in gene expression (mRNA), variations of DNA (copy number) and next generation NGS with application in cancer imunoteraphy and searching for biomarkers. This field is in the priority health and quality of life of the National strategy for scientific investigation 2020;
- Bi-characteristic curves for some problems arising in geophysics. This field has effect in the priorities security and environment of Horizon 2020;
- Studying of the perturbations of limit cycles and pico technology. This field is in the priority new technologies of the National strategy for scientific investigations 2020.

### Scientific Projects of the Department:

- Differential equations, equations of mathematical physics and applications –scientific leader Prof. D.Sci. Angela Slavova;
- Integro-differential equations for solving coupled problems in multifunctional materials with nano-heterogeneities – scientific leader Prof. D.Sci. Tsviatko Rangelov;
- Theoretical and Numerical Investigation of Nonlinear Mathematical Models – scientific leader Prof. D.Sci. Nikolaj Kutev.

- Details
- Category: Differential Equations and Mathematical Physics
- Created: 18 June 2017
- Hits: 410

### 2016 - 2017

**14.06.2017 ** at 14:00 in room 478 of IMI-BAS, Vasil Tinchev Ph.D., „SHADOWS OF SELF GRAVITATING COMPACT OBJECTS“

**17.05.2017 ** at 14:00 in room 478 of IMI-BAS, Prof. Tsvyatko Rangelov, „LOWER ESTIMATE FOR THE FIRST EIGENVALUE OF R-LAPLACIAN“ (A. Fabrikant, N. Kutev, Ts. Rangelov)

**19.04.2017 ** at 14:00 in room 478 of IMI-BAS, Dragomir Dragnev, Ph.D., „СИМПЛЕКSYMPLECTIC CAPACITIES AND SOME APPLICATIONS, PART 2“

**05.04.2017 ** at 14:00 in room 478 of IMI-BAS, Mirko Tarulli, Ph.D., „MORAWETZ AND INTERACTION MORAWETZ IDENTITIES FOR SYSTEMS OF N-DEFOCUSING WEAKLY COUPLED NLS EQUATIONS ON Rd × Mk IN LOW SPACE DIMENSIONS“

**15.03.2017 ** at 14:00 in room 478 of IMI-BAS, Assoc. Prof. Peter Rashkov, „MATHEMATICAL MODEL OF THE CELL POLARITY SYSTEM OF THE SOIL BACTERIA MYXOCOCCUS XANTHUS“

**01.03.2017 **at 14:00 in room 478 of IMI-BAS, Acad. Peter Popivanov, „NEW RESULTS FOR LINEAR OPERATORS OVER COMPACT MANIFOLDS, INCLUDING TORUSES “

**22.02.2017 **at 14:00 in room 478 of IMI-BAS, Galina Bobeva, „LOCAL ACTIVITY METHOD FOR REACTION-DIFFUSION EQUATIONS“

**15.02.2017 **at 14:00 in room 478 of IMI-BAS, Dragomir Dragnev, Ph.D., „SYMPLECTIC CAPACITIES AND SOME APPLICATIONS“

**08.02.2017 **at 14:00 in room 478 of IMI-BAS, Assoc. Prof. Filip Filipov, „STRUCTURAL METHODS FOR SOLVING SOME WAVE EQUATION BOUNDARY PROBLEMS“

**25.01.2017 **at 14:00 in room 478 of IMI-BAS, Acad. Peter Popivanov, „TWO PROBLEMS OF PDEs“

**14.12.2016 ** from 13:00 to 17:00 h. in room 478 of IMI-BAS, DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS DEPARTMENT ANNUAL SEMINAR 2016

**16.11.2016 **at 14:00 in room 478 of IMI-BAS, Alexander Stefanov, Ph.D., „GENERAL RELATIVITY THEORY AND GRAVITATIONAL WAVES“

**26.10.2016 ** at 14:00 in room 478 of IMI-BAS, Prof. Vladimir Gerdzhikov, „ON THE REDUCTIONS OF MULTICOMPONENT NONLINEAR SCHRÖDINGER EQUATIONS“

**19.10.2016 - 21.10.2016 **, from 14:00 to 15:00 h. in room 478 of IMI-BAS, Dr. Monica Marras, University of Cagliari, Department of Mathematics and Computer Science, PHD Course on „Qualitative Properties of Solutions to Nonlinear Parabolic Boundary Value Problems“

**28.09.2016 **at 14:00 in room 478 of IMI-BAS, Acad. Peter Popivanov, „THE NASH-MOSER THEOREM“

### 2015 – 2016

**22.06.2016 **at 14:00 in room 478 of IMI-BAS, preliminary defense of the following thesis of PhD student Todor Petkov Mitev, with mentor Prof. Georgi Popov, „NORMAL FORMS AND SPECTRAL ASYMPTOTICS“

**15.06.2016 ** at 14:00 in room 478 of IMI-BAS, Prof. D.Sc. Venelin Zhivkov, „A NUMERICAL EXAMPLE FOR APPLICATION OF CONTINUOUS WAVELET TRANSFORM“

**08.06.2016 ** at 14:00 in room 478 of IMI-BAS, Assoc. Prof. Georgi Boyadzhiev, Ph.D., „PRINCIPLE OF COMPARISON FOR QUASI-LINEAR ELIPTICAL AND PARABOLIC SYSTEMS AND APPLICATIONS. 3D MODELS OF EARTH CRUST AND UPPER MANTLE BY BI-CHARACTERISTICS.“

**20.04.2016 **at 14:00 in room 478 of IMI-BAS, Todor Mitev from Rouse University, „NORMAL FORMS IN GEVRAY CLASSES AND SPECIAL ASYMPTOTICS“

**13.04.2016 **at 14:00 in room 478 of IMI-BAS, Yuri Dimitrov from Rouse University, „APPROXIMATIONS OF FRACTIONAL INTEGRALS AND FRACTIONAL DERIVATIVES. NUMERICAL METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS“

**23.03.2016 **от 14:30 ч., зала 478, Prof. Vladimir Gerdzhikov, „ON THE LOCAL AND NON-LOCAL MODELS OF THE KULISH-SKLYANIN TYPE“

**16.03.2016 **at 14:00 in room 478 of IMI-BAS, Sen. Assist. Prof. Tihomir Valchev, „NON-LINEAR PDE IN CLASSICAL DIFFERENTIAL GEOMETRY“

**24.02.2016 ** at 14:00 in room 478 of IMI-BAS, Acad. Peter Popivanov, „EXPLOSIVE SOLUTIONS OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS IN GEOMETRY“

**17.02.2016 **at 14:00 in room 478 of IMI-BAS, Prof. Vladimir Gerdzhikov: „ON THE SOLITON SOLUTIONS OF EQUATIONS OF TITEICA TYPE“

**10.02.2016 ** at 14:00 in room 478 of IMI-BAS, Assist. Prof. Alexander Stefanov (Institute of Mathematics and Informatics) and Assist. Prof. Stanislav Varbev (Institute of Solid State Physics): „NON-LINEAR DYNAMIC SYSTEMS WITH INFINITE -DIMENSIONAL LIE ALGEBRAS“

**13.01.2016 **от 13:00 ч., зала 478, Acad. Peter Popivanov: „VLASOV EQUATION, LANDAU DAMPING, ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR INITIAL PROFILE VERY CLOSE TO THE ANALYTIC ONE THROUGH THE EYES OF CEDRIC VILLANI (FIELDS MEDAL WINNER IN 2010)“

**16.12.2015 **from 10:00 to 17:00 h. in room 478 of IMI-BAS, Annual Reporting Seminar of Differential Equation and Mathematical Physics Department. Dedicated to the memory of Prof. Todor Gramchev (1956-2015).

**02.12.2015 ** at 14:00 in room 478 of IMI-BAS, G. Botadjiev: „The Ito Integral and Its Applications to Economics“; G. Chobanov: „Stohastic Differential Equations“

**28.10.2015 ** at 14:00 in room 478 of IMI-BAS, Dobromir Kralchev: „PROOF OF THE IRRATIONALITY OF ZETA(3)“

**21.10.2015 **at 14:00 in room 478 of IMI-BAS, Alexander Stefanov: „POSITIVE MAPPINGS BETWEEN С*-ALGEBRAS AND APPLICATIONS IN QUANTUM INFORMATION“

**07.10.2015** at 14:00 in room 478 of IMI-BAS, Prof. Nikolay Kutev (co-authors: N. Kolkovska and M. Dimova): „ORBITAL STABILITY OF SOLITONS ON PROPAGATION OF NERVE IMPULSES IN BIOMEMBRANES“

**23.09.2015** at 14:00 in room 478 of IMI-BAS, Acad. Peter Popivanov: „PSEUDO-DIFFERENTIAL OPERATORS OF SUBPRINCIPAL TYPE: OLD AND NEW SOLVABILITY RESULTS“