Dissipative Dynamical Systems with Periodic Kick Actions and Their Global Attractors

Student: Galyautdinov Damir

Supervisor: Vladimir V. Chepyzhov

Educational Programme: Mathematics (Bachelor)

Final Grade: 7

Year of Graduation: 2024

In this paper, we study the structure of uniform global attractors of processes generated by non-autonomous differential equations, the key feature of which is periodic impulse effects in the form of delta functions. And although due to this feature the processes under consideration cease to be continuous, conditions are found under which the system is dissipative. For such equations, the existence of a uniform attractor is proved, and its structure is described. This result is also illustrated by examples of compressive processes and a finite-dimensional analogue of the Navier-Stokes system.

Full text (added June 2, 2024)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses