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Nonclassical problems of mathematical physics

Обов’язкова дисципліна для ОП

Second

2023/2024

4 Semester

5

PLO1. Be able to use of in-depth professional knowledge and practical skills to optimize the design of models of any complexity, to solve specific problems of designing intelligent information systems of different physical nature. PLO10. Be able to build models of physical and production processes, design of storage and data space, knowledge base, using charting techniques and standards for information systems development.

To successfully learn the discipline “Nonclassical problems of mathematical physics” the student should satisfy the following requirements. They have successfully passed the courses Calculus, Functional Analysis, and Equations of Mathematical Physics. They know (a) fundamentals of Calculus, Functional Analysis, and Equations of Mathematical Physics. They can (a) apply fundamentals of Calculus, Functional Analysis, and Equations of Mathematical Physics to solve practical problems. They should be able to (a) seek information in the Internet.

Block 1. Fundamentals Distributions Rigged Hilbert spaces Sobolev spaces Weak solutions of initial-boundary problems Galerkin method and its analogues Optimal control and system controllability Control work Block 2. Nonclassical problems Weak solvability of pseudoparabolic systems Galerkin methods analogues for pseudoparabolic systems Pulse optimal control of pseudoparabolic systems Weak solvability of pseudohyperbolic systems Galerkin method analogues for pseudohyperbolic systems Pulse optimal control of pseudohyperbolic systems Weak solvability of Sobolebʼs systems Galerkin method analogues for Sobolevʼs systems Pulse optimal control of Sobolevʼs systems Barenblatt–Zheltov–Kochina model Control work

1. Lyashko S.I. Obobschennoe upravlenie lineynyimi sistemami. K.: Nauk. dumka, 1998. 2. Vragov, V.N. Kraevyie zadachi dlya neklassicheskih uravneniy matematicheskoy fiziki. Novosibirsk: NGU, 1983. 3. Vladimirov V.S. Uravneniya matematicheskoy fiziki. M.: Nauka, 1981. 4. Korpusov M.O., Sveshnikov A.G. Nelineynyiy funktsionalnyiy analiz i matematicheskoe modelirovanie v fizike. M.: Krasand, 2011. 5. Sveshnikov A.G, Alshin A.B., Korpusov M.O., Pletner Yu.B. Lineynyie i nelineynyie uravneniya sobolevskogo tipa. M.: Fizmatlit, 2007.

Lectures, independent work, recommended literature processing, homework.

Intermediate assessment: The maximal number of available points is 60. Test work no. 1: RN 1.1, RN 1.2 – 30/18 points. Test work no. 2: RN 1.1, RN 1.2 – 30/18 points. Final assessment (in the form of final test): The maximal number of available points is 40. The results of study to be assessed are RN 1.1, RN 1.2, RN 2.1, and RN 3.1. The form of final test: writing. The types of assignments are 3 writing assignments (2 theoretical and 1 practical).

Ukrainian