Inverse Problems for Integro-differential Operators
Springer International Publishing (Verlag)
978-3-031-89141-0 (ISBN)
Inverse problems lie at the core of scientific discovery, enabling us to determine causes from observed consequences. They are fundamental to both theoretical research and technological innovation, making them a central topic in the mathematical sciences. This book explores a cutting-edge area of inverse problems those related to integro-differential operators, also known as nonlocal operators. Due to their unique theoretical properties and vast practical applications, nonlocal inverse problems have garnered significant interest in recent years, making this an ideal time for a dedicated research monograph.
Focusing on nonlocality in space, this book provides a systematic study of both forward and inverse problems associated with integro-differential operators. It introduces key properties of forward problems well-posedness, maximum principles, and unique continuation before delving into inverse problems, including modeling, unique identifiability, stability analysis, and reconstruction methods. The discussion bridges mathematical theory with real-world applications, offering insights into pioneering contributions as well as recent advances by the authors and their collaborators.
As an evolving field, nonlocal inverse problems present a wealth of open challenges and emerging applications. This book not only provides a comprehensive introduction but also aims to inspire future research with fresh perspectives and novel insights. It is an invaluable resource for graduate students and early-career researchers looking to enter the field, as well as a valuable reference for experienced mathematicians working in inverse problems and mathematical analysis.
Hongyu Liu is Chair Professor of Applied Mathematics at City University of Hong Kong, Hong Kong. He worked as a Professor and the Associate Head at the Department of Mathematics, Hong Kong Baptist University (2014--2020). Prior to that, he held faculty positions at University of North Carolina, Charlotte, USA (2011--2014), University of Reading, UK (2010/11), and University of Washington, Seattle, USA (2007--2010). He obtained his PhD in Mathematics from The Chinese University of Hong Kong (2007). His research focuses on the analysis, computations and applications of inverse problems and imaging, wave propagation, partial differential equations, mathematical materials science, scattering theory and spectral theory, game theory and mathematical biology. He has published nearly 200 peer-reviewed research papers in leading journals, and in addition he coauthored 4 books/research monographs by Springer and Soc. Math. France. He is recipient of the Calderón Prize of Inverse Problems International Association; the Changjiang Chair Professorship of Ministry of Education of China; and is Fellow of IOP and Fellow of IMA. He is an ISI Highly Cited Researcher by Clarivate in 2024.
Yi-Hsuan Lin is an Assistant Professor of Applied Mathematics working at National Yang Ming Chiao Tung University (2019-now), Taiwan. Prior to this, he graduated from National Taiwan University under Prof. Jenn-Nan Wang s supervision in 2016, and he was a postdoc working with Prof. Gunther Uhlmann and Prof. Mikko Salo. His research field focuses on inverse problems for PDEs and nonlocal problems, and he and his collaborators developed many methods, such as higher-order linearization schemes for nonlinear elliptic equations. He also contributed several important works for nonlocal inverse problems, such as variable coefficients nonlocal operators, monotonicity methods, the nonlocal Schiffer problem, and local-nonlocal reductions. He published nearly 35 peer-reviewed research papers in leading journals. He has been elected as an Alexander von Humboldt Research Fellow (for experienced researcher, since 2024) at the University of Duisburg-Essen, Germany. He is also a recipient of the EAIP Young Scientist Award of the Eurasian Association on Inverse Problems in 2024.
Preface.- Introduction.- Integro-differential operators.- Part 1. Inverse problems for linear integro-differential operators.- Inverse problems for the fractional Schr¨odinger equation.- Inverse problems for the fractional Schr¨odinger equation with drift.- Inverse problems for variable coefficients nonlocal equations.- Inverse problems for the fractional wave equation.- Part 2. Inverse problems for nonlinear integro-differential operators.- Inverse problems for fractional semilinear elliptic equations.- Montonicity-based inversion formula with power type
nonlinearities.- Summary and some open questions.- Bibliography.
| Erscheinungsdatum | 13.05.2025 |
|---|---|
| Reihe/Serie | Applied Mathematical Sciences |
| Zusatzinfo | XIV, 304 p. 3 illus., 1 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | Fractional PDEs • integro-differential operators • Inverse Problems • Modelling • Nonlocal operators • Reconstruction Methods • stability estimates • unique identifiability |
| ISBN-10 | 3-031-89141-4 / 3031891414 |
| ISBN-13 | 978-3-031-89141-0 / 9783031891410 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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