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Author: Massimo Cicognani Publisher: Springer Nature ISBN: 3030613461 Category : Mathematics Languages : en Pages : 469
Book Description
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.
Author: Massimo Cicognani Publisher: Springer Nature ISBN: 3030613461 Category : Mathematics Languages : en Pages : 469
Book Description
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.
Author: Massimo Cicognani Publisher: ISBN: 9783030613471 Category : Languages : en Pages : 0
Book Description
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.
Author: Victor Isakov Publisher: Springer ISBN: 3319516582 Category : Mathematics Languages : en Pages : 414
Book Description
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.
Author: Bilal Abbasi Publisher: ISBN: Category : Languages : en Pages :
Book Description
"The goal of this dissertation is to explore and demonstrate the applications of numerical methods for elliptic partial differential equations (PDEs). The numerical methods presented, as we will see, are applicable in a variety of contexts, ranging from computational geometry to machine learning. The general analytic framework of this dissertation is viscosity solutions for elliptic PDEs. The corresponding numerical framework belongs to Barles and Souganidis, with emphasis on its reinterpretation using elliptic finite difference schemes in lieu of monotone schemes. The first problem considered was building a multi-criteria anomaly detection algorithm that can be applied in a real-time setting. The algorithm was centered around a recently discovered PDE continuum limit for nondominated sorting. By exploiting the relatively low computational cost of numerically approximating the PDE we developed an efficient method to detect anomalies in two-dimensional data in real-time. We also derived a transport equation which characterizes sorting points within nondominated layers. This allowed us to add to our algorithm the ability of classifying anomalies. Our algorithm has an inherent ability to adapt to changes in the trend of data. In addition to demonstrating the effectiveness of our algorithm on synthetic and real data, we presented probabilistic arguments proving convergence rates for the PDE-based ranking.The second problem addressed the issue of computing the quasiconvex envelope of a given function. In a series of papers written by Barron, Goebel, and Jensen, first- and second-order differential operators characterizing quasiconvexity were rigourously developed. These characterizations, arising in the form of PDEs, unfortunately prove intractable in light of existing numerical methods. Hence, attempting to generate the quasiconvex envelope using these operators with an obstacle term, in a manner similar to Oberman, is not prudent. Our solution to this, and consequently our contribution, came two-fold (each of which is its own article, respectively): (i) a first-order nonlocal line solver which can compute the quasiconvex envelope in one dimension, and for which the extension to arbitrary dimensions follows naturally; (ii) a second-order operator which offers a more relaxed notion of quasiconvexity, and is more obliging to numerical approximation. Convergence of the algorithms presented in both solutions is proven, and numerical examples validating the arguments presented therein are demonstrated." --
Author: Luiz Roberto Evangelista Publisher: Cambridge University Press ISBN: 1108663486 Category : Science Languages : en Pages : 361
Book Description
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.
Author: Bruno Carpentieri Publisher: BoD – Books on Demand ISBN: 1839686561 Category : Mathematics Languages : en Pages : 374
Book Description
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.
Author: Grigorij Kulinich Publisher: Springer Nature ISBN: 3030412911 Category : Mathematics Languages : en Pages : 240
Book Description
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.
Author: Giampiero Esposito Publisher: Springer ISBN: 3319575449 Category : Mathematics Languages : en Pages : 428
Book Description
This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.
Author: Massimo Cicognani
Author: Massimo Cicognani
Author: Massimo Cicognani
Author: Victor Isakov
Author: Bilal Abbasi
Author: Heinz-Dieter Neumann
Author: Luiz Roberto Evangelista
Author: Bruno Carpentieri
Author: Grigorij Kulinich
Author: David L. Colton
Author: Giampiero Esposito