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.
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