Фанкина И.В. «Асимптотический анализ задачи о сопряжении включений Бернулли–Эйлера и Тимошенко в упругом теле» Сибирские электронные математические известия, 22, № 1, с. 326-342 (2026)

We consider the equilibrium problem for a 2D elastic body with two thin elastic inclusions with a junction at a point. It is assumed that a crack exists between the inclusions and the body. Inequality-type boundary conditions are imposed at the crack faces to prevent mutual penetration. The problem depends on rigidity parameter of one of the inclusions: we are talking about family of problems. A weak convergence of solutions of the family of problems in suitable functional spaces is proved. By this convergence, we pass to the limit in the problems and establish the form of limit problem. Strong convergence of solutions of family of problems is also established. On its basis, the existence of a solution of the optimal control problem is proved. The optimal control problem is formulated in accordance with the Griffiths failure criterion, the control parameter is the rigidity parameter of the inclusion.

Vasyukov A.V., Petrov I.B. «On the aberrations correction in ultrasound images in case of heterogeneous media» Сибирские электронные математические известия, 22, № 1, с. А18-А19 (2026)

This paper is devoted to a possible approach to aberrations correction in ultrasound images in case of heterogeneous media. Numerical modeling is performed for a direct problem - obtaining synthetic numerical ultrasound images using known geometry and rheology of the region, as well as transducer parameters. The numerical images reproduce distortions and artifacts that are typical for a medium containing areas with significantly different sound speeds. Convolutional neural networks are used to locate the interface of acoustically contrasting media. The located interfaces between areas with significantly different sound speeds are used to improve the quality of the image. The results of the present work demonstrate that it is possible to improve the quality of images using reasonably fast algorithms based solely on information from the ultrasound sensor. The discussion section of the paper mentions the problems that should be addressed to allow future hardware implementation of the proposed approach.

Ильичев А.Т., Савин А.С. «О движении жидких частиц под ледяным покровом» Сибирские электронные математические известия, 22, № 1, с. А121-А125 (2026)

A fluid layer of finite depth is described by Euler's equations governing the motions of the ideal fluid (water). The ice is assumed to be solid and it freely floats on the water surface. The ice cover is modeled by a geometrically non-linear elastic Kirchhoff–Love plate. The trajectories of liquid particles under the ice cover are found in the field of different nonlinear surface traveling waves of small, but finite amplitude. These waves are: the classical solitary wave of depression, existing on the water-ice interface when the initial stress in the ice cover is large enough, the generalized solitary wave, the envelope solitary wave and the so-called dark soliton. The last two waves indicate the focusing or defocusing of nonlinear carier surface wave, the generalized solitary wave consists of solitary wave core and periodic asymptotic wave at spacial infinity, moreover for the algebraically small amplitude of the wave core the amplitude of the mentioned above periodic wave is exponentially small. The consideration is based on explicit asymptotic expressions for solutions describing the mentioned wave structures on the water-ice interface, as well as asymptotic solutions for the velocity field in the liquid column corresponding to these waves.