Kernel Determination Problems in Hyperbolic Integro-Differential Equations
Kernel Determination Problems in Hyperbolic Integro-Differential Equations

Author: Durdimurod K. Durdiev

Publisher: Springer Nature

Published: 2023-06-18

Total Pages: 390

ISBN-13: 9819922607

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This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional “impacts” or “explosions”. This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.

Identification Problems of Wave Phenomena
Identification Problems of Wave Phenomena

Author: A. Lorenzi

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 352

ISBN-13: 3110943298

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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Inverse Problems and Related Topics
Inverse Problems and Related Topics

Author: Gen Nakamura

Publisher: CRC Press

Published: 2000-02-28

Total Pages: 268

ISBN-13: 9781584881919

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Inverse problems arise in many disciplines and hold great importance to practical applications. However, sound new methods are needed to solve these problems. Over the past few years, Japanese and Korean mathematicians have obtained a number of very interesting and unique results in inverse problems. Inverse Problems and Related Topics compiles papers authored by some of the top researchers in Korea and Japan. It presents a number of original and useful results and offers a unique opportunity to explore the current trends of research in inverse problems in these countries. Highlighting the existence and active work of several Japanese and Korean groups, it also serves as a guide to those seeking future scientific exchange with researchers in these countries.

Volterra Equations and Inverse Problems
Volterra Equations and Inverse Problems

Author: A. L. Bughgeim

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 216

ISBN-13: 3110943247

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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Nonlinear Differential Equations and Dynamical Systems
Nonlinear Differential Equations and Dynamical Systems

Author: Feliz Manuel Minhós

Publisher: MDPI

Published: 2021-04-15

Total Pages: 158

ISBN-13: 3036507108

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This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Volterra Integral Equations
Volterra Integral Equations

Author: Hermann Brunner

Publisher: Cambridge University Press

Published: 2017-01-20

Total Pages: 405

ISBN-13: 1316982653

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This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.