## Department

# Differential Equations and Mathematical Physics

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).

*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.