Department of Higher Mathematics


PhD thesis defense

We invite to defend the PhD thesis of the assistant of the department of HM by Olha V. Zhyla

The defense will take place on June 6 at 1.00 pm at a meeting of the specialized academic council 64.052.03 of the Kharkov National University of Radio Electronics at the address: 14, Nauky Ave., Kharkov, Ukraine, meeting room.

PhD thesis: Integral equation method in modeling of asymmetric electromagnetic phenomena in an inhomogeneous medium.


    An actual scientific problem on electromagnetic pulse transformation in a non-uniform and non-stationary environment is solved. For the first time the transformation of the Airy electromagnetic pulse as a result of normal falling on a flat dielectric boundary is investigated. The solution is obtained by the Voltaire integration method. It is shown that nature of distribution of the transmitted and reflected impulses is controlled by a starting parameter value. The case when the boundary begins uniform movement towards to the pulse and gradually achieves value of the pulse’s speed is investigated in details. The exact problem of interaction of the Airy pulse with a dielectric layer is solved. The analysis of the field in a layer depending on the observation point position and a case with one and two boundaries (layer) is performed. Exact expressions describing distribution of the Airy pulse in a dielectric layer which boundaries move uniformly are analyzed. The comparative analysis with the results obtained for a layer with constant boundaries is carried out.

Keywords: dielectric layer, non-stationary environment, Volterra integral equation, resolvent, Airy pulses.