Open access peer-reviewed Edited Volume

Mathematical Theorems

Lyudmila Alexeyeva

Institute of Mathematics and Mathematical Modeling


mathematical theorem fundamental solution boundary value problem hyperbolic equation hyperbolic equations system mathematical physics equation generalized solution green function green tensor mathematical physics

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About the book

This book covers the field of mathematical physics, the mechanics of a deformable solid, and wave dynamics of media. It will discuss the developed mathematical models, and methods, for investigation of the dynamic processes in solids and in media. Its content includes the methods of generalized functions and boundary integral equations for solving boundary value problems for systems equations of hyperbolic type of mathematical physics; BIE method for solving stationary and non-stationary boundary-value problems of elastodynamics, electrodynamics and field theory. The fundamental and generalized solutions of considered equations are constructed and their properties are studied. Green functions and Green tensors for the systems are presented and methods of their construction on the base Fourier and Laplace transformation, are given.
The application of these equations and their solutions to solving boundary value problems are developed on the base of analytic mathematical methods.

This book may be useful to specialists in the fields of mathematics, mathematical physics and mechanics.

Publishing process

Book initiated and editor appointed

Date completed: November 7th 2019

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: May 23rd 2020

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: August 11th 2020

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: October 10th 2020

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About the editor

Lyudmila Alexeyeva

Institute of Mathematics and Mathematical Modeling

The doctor of physical and mathematical sciences professor Alexeyeva Lyudmila Alexeyevna is the famous highly qualified specialist in the field of mathematical physics, mechanics, applied mathematics, dynamics of constructions. Now she is the chief researcher of Institute of Mathematics and mathematical modeling and professor of mechanics and Mathematics Faculty of Al Farabee University in Almaty in Kazakhstan. She was born on January 12, 1947 in the city Kaliningrad (USSR, Russia Federation) in family of therapist doctors. The family had three daughters, Lyudmila - the eldest. Childhood was spent in frequent journeys in connection with the service of his father. In 1954 she entered the Soviet secondary school in the city of Yuterbog (DDR) at her father’s place of employment, in 1965 she graduated with a gold medal in the 11th grade of secondary school in the city Murom, Vladimir region. In the same year, Lyudmila entered the Faculty of Mechanics and Mathematics of M.V. Lomonosov Moscow State University (Moscow, USSR). She was Lenin scholarship for 4-5 courses. In October 1970, she enrolled in the postgraduate program Mech-Mat. Faculty of Moscow State University, specialized in the Department of Theoretical Mechanics under the guidance of Corresponding Member of the USSR Academy of Sciences D.Ye. Okhotsimsky. PhD thesis on the topic “Modeling the dynamics and motion control of a walking apparatus” in the specialty 01.02.01. - theoretical mechanics - defended at Moscow State University in 1976. After graduating from postgraduate school in 1973, she with husband were assigned to work in Alma-Ata at the Institute of Mathematics and Mechanics of the Academy of Sciences of the Kazakh SSR. Here she worked in the laboratory of the theory of seismic stability of underground structures as junior researcher (1976-1977), senior researcher (1978-1987), general research associate (1988-1991). In 1991 she defended her doctoral thesis “Dynamics of Extended Underground Structures” at the Institute of Mathematics and Mechanics of the Academy of Sciences of the Kazakh SSR for the degree of Doctor of Physical and Mathematical Sciences in specialty 01.02.07 - soil mechanics, rocks and massive media . In 1992, also the USSR Higher Attestation Commission awarded her the title of professor of mechanics in the specialty 01.02.04 - mechanics of a deformable solid. In 1992, the Institute of Theoretical and Applied Mathematics was organized. Since then she has been working at this institute. At first she worked as the head of the laboratory of wave dynamics (1992-2012), from 20012 to 2018 she was the head of the Department of Mathematical Physics and Modeling at this institute. Now she works as the chief researcher of this department, the head of a research project. Currently this institute is called the Institute of Mathematics and Mathematical Modeling Concurrently, she has been working for more than 20 years as a professor at the Faculty of Mechanics and Mathematics at the Al Farabi Kazakh National University. She teaches in graduate and doctoral studies. For scientific activity she received the State Scientific Scholarship for scientists and specialists who made an outstanding contribution to the development of science and technology in 1997-2000, 2000-2002, 2004-2006, 2008-2010; awarded the Insignia for workers of science and education of the Republic of Kazakhstan. She is the member of European Mechanics Sosciety and the member of the International Academy of Sciences of Eurasia.

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