Parabolic Equations with Irregular Data and Related Issues
Parabolic Equations with Irregular Data and Related Issues

Author: Claude Le Bris

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-06-17

Total Pages: 158

ISBN-13: 311063550X

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This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

Parabolic Equations with Irregular Data and Related Issues
Parabolic Equations with Irregular Data and Related Issues

Author: Claude Le Bris

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-06-17

Total Pages: 242

ISBN-13: 3110633140

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This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods
Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods

Author: Alexander V. Bobylev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-09-23

Total Pages: 212

ISBN-13: 3110551004

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This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.

Finite Difference Methods for Nonlinear Evolution Equations
Finite Difference Methods for Nonlinear Evolution Equations

Author: Zhi-Zhong Sun

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-05-08

Total Pages: 432

ISBN-13: 3110796015

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Introduces recent research results of finite difference methods including important nonlinear evolution equations in applied science. The presented difference schemes include nonlinear difference schemes and linearized difference schemes. Features widely used nonlinear evolution equations such as Burgers equation, regular long wave equation, Schrodinger equation and more. Each PDE model includes details on efficiency, stability, and convergence.

Metamaterial Analysis and Design
Metamaterial Analysis and Design

Author: Habib Ammari

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-11-06

Total Pages: 122

ISBN-13: 3110784963

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Metamaterials are advanced composite materials which have exotic and powerful properties. Their complicated microstructures make metamaterials challenging to model, requiring the use of sophisticated mathematical techniques. This book uses a from-first-principles approach (based on boundary integral methods and asymptotic analysis) to study a class of high-contrast metamaterials. These mathematical techniques are applied to the problem of designing graded metamaterials that replicate the function of the cochlea.

Numerical Simulation of Incompressible Viscous Flow
Numerical Simulation of Incompressible Viscous Flow

Author: Roland Glowinski

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-09-19

Total Pages: 232

ISBN-13: 3110785013

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This text on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to split complicated computational fluid dynamics problems into a sequence of simpler sub-problems. A methodology for solving more advanced applications such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid is also presented.

Neural Networks and Numerical Analysis
Neural Networks and Numerical Analysis

Author: Bruno Després

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-08-22

Total Pages: 174

ISBN-13: 3110783185

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This book uses numerical analysis as the main tool to investigate methods in machine learning and A.I. The efficiency of neural network representation on for polynomial functions is studied in detail, together with an original description of the Latin hypercube method. In addition, unique features include the use of Tensorflow for implementation on session and the application n to the construction of new optimized numerical schemes.

Richardson Extrapolation
Richardson Extrapolation

Author: Zahari Zlatev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2017-11-07

Total Pages: 310

ISBN-13: 3110533006

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Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book. Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. Contents The basic properties of Richardson extrapolation Richardson extrapolation for explicit Runge-Kutta methods Linear multistep and predictor-corrector methods Richardson extrapolation for some implicit methods Richardson extrapolation for splitting techniques Richardson extrapolation for advection problems Richardson extrapolation for some other problems General conclusions

Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition
Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition

Author:

Publisher: ScholarlyEditions

Published: 2013-05-01

Total Pages: 1173

ISBN-13: 1490108580

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Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Applied Analysis. The editors have built Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Analysis in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Superlinear Parabolic Problems
Superlinear Parabolic Problems

Author: Pavol Quittner

Publisher: Springer Science & Business Media

Published: 2007-12-16

Total Pages: 593

ISBN-13: 3764384425

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This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.