### Levashova N.T. Nefedov N. Nikolaeva O. Orlov A.O.

## The solutions with internal transition layers in the boundary value problems with discontinuous inhomogeneities

### Reporter: Levashova N.T.

THE SOLUTIONS WITH INTERNAL TRANSITION LAYERS IN THE BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS INHOMOGENEITIES

N. T. Levashova 1, N. N. Nefedov 1, O. A. Nikolaeva 1, A. O. Orlov1

Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow

natasha@npanalytica.ru, nefedov@phys.msu.ru, nikolja3004@gmail.com, orlov.andrey@physics.msu.ru

The authors studied the existence of solutions with internal transition layers of boundary value problems for the second order equations with discontinuity in the right-hand side. Boundary value problems in a similar formulation can be used for mathematical modeling of various physical characteristics in layered semiconductor structures or close to the boundary layer between different environments, for example, temperature in the surface layer of the ocean. The study of such boundary value problems is a necessary component of mathematical modeling of various physical characteristics in the environments with discontinuous characteristics. The authors studied the smooth solution of the boundary problem for the Laplace equation and the solution of the problem on the segment undergoing the jump of the derivative.

The project has been partially supported by grant of the Russian Foundation for Basic Research (RFBR 13–01–00200).

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