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Anomalies in Partial Differential Equations

Author: Massimo Cicognani

Publisher: Springer Nature

Published: 2021-02-03

Total Pages: 469

ISBN-13: 3030613461

The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in the action of localizing operators or the description of wave front sets, complete the volume.

Anomalies in Partial Differential Equations

Author: Massimo Cicognani

Publisher:

Published: 2021

Total Pages: 0

ISBN-13: 9783030613471

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Inverse Problems for Partial Differential Equations

Author: Victor Isakov

Publisher: Springer

Published: 2017-02-24

Total Pages: 406

ISBN-13: 3319516582

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A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

Fractional Diffusion Equations and Anomalous Diffusion

Author: Luiz Roberto Evangelista

Publisher: Cambridge University Press

Published: 2018-01-25

Total Pages: 361

ISBN-13: 1108663486

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Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

Author: Grigorij Kulinich

Publisher: Springer Nature

Published: 2020-04-29

Total Pages: 240

ISBN-13: 3030412911

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This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.

Congenital Anomalies of Coronary Arteries

Author: Gianfranco Butera

Publisher: Springer Nature

Published: 2023-11-21

Total Pages: 279

ISBN-13: 3031369661

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The coronaries are the first branches of the ascending aorta. They arise from their respective sinuses of Valsalva, and gradually branch distally to the myocardium. Abnormalities of the coronary arteries, either congenital or acquired, can be characterized as a lack of origin, abnormal origin, anomalous course, lack of patency, abnormal connections, and/or abnormal drainage of the coronary vessels. Interruptions to or lack of flow can cause significant morbidity and mortality due to ischemia, infarction and fistulous connections, which can lead to cardiac failure, endocarditis and ischemia. Coronary artery anomalies are rare in general populations. Although they can be benign and asymptomatic, they can also be malignant due to their origin and course and can cause sudden cardiac death. As such, an understanding of how to analyze, diagnose and treat them is vital. This book presents the latest advances in congenital anomalies of coronary arteries. It offers a comprehensive overview of the field, including illustrative angiograms and diagrams that demonstrate all possible anomalies and clarify what is abnormal, and also provides practical insights to guide practitioners in their everyday practice.

Introduction to Manual Medicine

Author: Heinz-Dieter Neumann

Publisher:

Published: 1989

Total Pages: 109

ISBN-13: 9780387506128

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High Accuracy Algorithm for the Differential Equations Governing Anomalous Diffusion

Author: Weihua Deng

Publisher: World Scientific Publishing Company

Published: 2019

Total Pages: 0

ISBN-13: 9789813142206

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The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models. The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model -- Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.

Temporal Climatology and Anomalous Weather Analysis

Author: Weihong Qian

Publisher: Springer

Published: 2017-02-20

Total Pages: 687

ISBN-13: 9811036411

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By breaking down atmospheric variables into temporal climatologies and anomalies, this book demonstrates that all weather extremes and climatic events are directly associated with the anomaly component of atmospheric motion. We can use the anomaly-based synoptic chart and dynamical parameters to objectively describe these extremes and events. The conception and differences of weather, climate and general circulation tend to confuse us, because there are no clear physical definitions available for them. Weather extremes such as heat waves, cold surges, freezing rains, heavy rains, severe drought, unusual storm tracks, and tornados are common on our planet’s surface. Climatic events such as Arctic warming and declining sea ice have become hot topics in recent years. An approach based on breaking down total variables into temporal climatologies and anomalies can be used to identify general circulation, analyze climatic anomalies and forecast weather extremes. Accordingly, this book will appeal to students, teachers and forecasters in the field of weather and climate alike.

Recent Developments in the Solution of Nonlinear Differential Equations

Author: Bruno Carpentieri

Publisher: BoD – Books on Demand

Published: 2021-09-08

Total Pages: 374

ISBN-13: 1839686561

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Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.