Overview
- Discusses the challenges of using observed data to estimate the values of unknown parameters to characterize a system
- Highlights the direct problems, such as initial problems (Cauchy problems) and initial-boundary value problems
- Presents new results on determining coefficients, convolution kernels and right-hand sides of time-fractional diffusion
Part of the book series: Industrial and Applied Mathematics (INAMA)
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About this book
This book discusses various inverse problems for the time-fractional diffusion equation, such as inverse coefficient problems (nonlinear problems) and inverse problems for determining the right-hand sides of equations and initial functions (linear problems). The study of inverse problems requires a comprehensive investigation of direct problems (such as representation formulas, a priori estimates and differential properties of the solution). This is particularly evident in nonlinear problems, where obtaining solvability theorems necessitates careful tracking of the exact dependence of the differential properties of the solution to the direct problem on the smoothness of the coefficients and other problem data. Therefore, a significant portion of the book is devoted to direct problems, such as initial problems (Cauchy problems) and initial-boundary value problems with various boundary conditions.
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Table of contents (7 chapters)
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Front Matter
Authors and Affiliations
About the author
Durdimurod K. Durdiev is Head of the Bukhara Branch of the Institute of Mathematics (named after V.I. Romanovskii) in the Academy of Sciences of the Republic of Uzbekistan, Uzbekistan. He is also Professor in the Department of Differential Equations, Bukhara State University, Uzbekistan. He is graduated from Novosibirsk State University, Russia, in 1990. In 1992, at this university, he defended his Ph.D. thesis in physical and mathematical sciences. Further, he defended his doctoral dissertation at the Institute of Mathematics and Information Technologies in Tashkent, in 2010, Uzbekistan. He teaches mathematical analysis, partial differential equations, calculus of variations and optimal control, theory of inverse problems of mathematical physics and theory of integral equations. His areas of scientific interest are in inverse problems for equations of mathematical physics, kernel determination inverse problems in integro-differential equations of hyperbolic and parabolic types, direct and inverse problems for equations with fractional derivatives.
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Bibliographic Information
Book Title: Inverse Problems for Fractional Diffusion Equations
Authors: Durdimurod K. Durdiev
Series Title: Industrial and Applied Mathematics
DOI: https://doi.org/10.1007/978-981-96-5338-6
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025
Hardcover ISBN: 978-981-96-5337-9Published: 16 June 2025
Softcover ISBN: 978-981-96-5340-9Due: 30 June 2026
eBook ISBN: 978-981-96-5338-6Published: 15 June 2025
Series ISSN: 2364-6837
Series E-ISSN: 2364-6845
Edition Number: 1
Number of Pages: XIV, 295
Number of Illustrations: 1 b/w illustrations