Generalized Functions Method in Boundary Value Problems for Wave Equations
暫譯: 波動方程邊界值問題中的廣義函數方法

Alexeyeva, Lyudmila, Bayegizova, Aigulim

Generalized Functions Method in Boundary Value Problems for Wave Equations
  • 出版商: Springer
  • 出版日期: 2026-01-14
  • 售價: $7,070
  • 貴賓價: 9.5 折 $6,717
  • 語言: 英文
  • 頁數: 154
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9819528011
  • ISBN-13: 9789819528011
  • 相關分類: 工程數學 Engineering-mathematics

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商品描述

This monograph presents the method of generalized functions and the method of boundary integral equations for solving nonstationary and stationary boundary value problems for classical hyperbolic equations of mathematical physics and electrodynamics: the wave equation, the Klein-Gordon equation, the Schrödinger equation and the system of Maxwell equations in spaces of dimension 1, 2, 3. It also discusses the theory of generalized functions for solving hyperbolic equations and systems described by pseudo-differential operators. The monograph studies the processes of shock waves, which is often simply impossible within the framework of the classical theory of differential equations. Generalized solutions of the considered boundary value problems, their regular integral representations and resolving singular boundary integral equations have been constructed, which belong to a new class of boundary integral equations, which can become the subject of a separate study in the field of functional analysis and function theory.

商品描述(中文翻譯)

本專著介紹了廣義函數方法和邊界積分方程方法，用於解決數學物理和電動力學的經典雙曲方程的非穩態和穩態邊界值問題：波方程、克萊因-戈登方程、薛丁格方程以及在一維、二維和三維空間中的麥克斯韋方程組。它還討論了用於解決由偽微分算子描述的雙曲方程和系統的廣義函數理論。本專著研究了衝擊波的過程，這在經典微分方程理論的框架內通常是無法實現的。考慮的邊界值問題的廣義解、其正則積分表示以及解決奇異邊界積分方程的方案已被構建，這些方案屬於一類新的邊界積分方程，可能成為功能分析和函數理論領域的獨立研究主題。

作者簡介

Lyudmila Alexeyeva is a Doctor of Physical and Mathematical Sciences, Professor, and now she is Chief Researcher at the Department of Mathematical Physics and Modeling at the Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan. For over 20 years, she worked as a professor at the Faculty of Mechanics and Mathematics at Al-Farabi Kazakh National University, and taught at the graduate and doctoral levels. She was born in Kaliningrad (1947, USSR, Russian Federation). In 1965, she graduated from high school in Murom, Vladimir Region, with a gold medal and entered the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University. From 1970 to 1973, she studied at a the postgraduate level of Faculty of Mechanics and Mathematics at this university, in the Department of Theoretical Mechanics.

Aigulim Bayegizova is Candidate of Physical and Mathematical Sciences (PhD), Senior Lecturer of the Department of Information Security of the Faculty of Information Technologies of the Eurasian National University named after L.N. Gumilyov, Astana, Kazakhstan, since 2024. She was born in the city Satpayev, Zhezkazgan region, Kazakhstan. In 1977, she graduated from 10th grade of Secondary School No. 19 in Satpayev. Then she entered the Faculty of Mechanics and Applied Mathematics of the Kazakh State University named after S.M. Kirov (Alma-Ata). After graduating from the university in 1982, she worked as an assistant in the Department of Higher Mathematics of the Zhezkazgan branch of the Karaganda Polytechnic Institute (1982-1990). Then she worked as the Head of the Department of Informatics and Computer Engineering of the Zhezkazgan Regional Department of Public Education (1990-1992). From 1998 to 2001, she studied in graduate school at the Department of Computer Engineering and Applied Mathematics of the Karaganda State University named after E.A. Buketov.

作者簡介(中文翻譯)

柳德米拉·阿列克謝耶娃是物理與數學科學博士、教授，目前擔任哈薩克斯坦阿拉木圖數學與數學建模研究所數學物理與建模系的首席研究員。她在阿法拉比哈薩克國立大學機械與數學系任教超過20年，教授研究生和博士生課程。她於1947年出生於加里寧格勒（蘇聯，俄羅斯聯邦）。1965年，她以金獎畢業於弗拉基米爾州穆羅姆的中學，並進入莫斯科國立大學的機械與數學系。1970年至1973年，她在該大學的機械與數學系理論力學專業攻讀研究生學位。 艾古林·巴耶吉佐娃是物理與數學科學候選人（博士），自2024年起擔任哈薩克斯坦以L.N. 古米廖夫命名的歐亞國立大學信息技術學院信息安全系的高級講師。她出生於哈薩克斯坦傑茲卡茲甘地區的薩特帕耶夫市。1977年，她從薩特帕耶夫的第19號中學畢業，然後進入以S.M. 基羅夫命名的哈薩克國立大學的機械與應用數學系。1982年大學畢業後，她在卡拉干達工業學院傑茲卡茲甘分院的高等數學系擔任助教（1982-1990）。隨後，她擔任傑茲卡茲甘地區公共教育部信息學與計算機工程系的主任（1990-1992）。1998年至2001年，她在以E.A. 布凱托夫命名的卡拉干達國立大學的計算機工程與應用數學系攻讀研究生學位。

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