Parabolic Equations With Irregular Data And Related Issues

Author : Claude Le Bris,Pierre-Louis Lions
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 49,8 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110635508

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Parabolic Equations with Irregular Data and Related Issues by Claude Le Bris,Pierre-Louis Lions Pdf

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.

Author : Claude Le Bris,Pierre-Louis Lions
Publisher : Walter de Gruyter GmbH & Co KG
Page : 264 pages
File Size : 41,6 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110633146

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Parabolic Equations with Irregular Data and Related Issues by Claude Le Bris,Pierre-Louis Lions Pdf

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.

Author : Guo Chun Wen
Publisher : World Scientific
Page : 256 pages
File Size : 40,7 Mb
Release : 1999-04-29
Category : Mathematics
ISBN : 9789814495035

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Linear And Nonlinear Parabolic Complex Equations by Guo Chun Wen Pdf

This book deals mainly with linear and nonlinear parabolic equations and systems of second order. It first transforms the real forms of parabolic equations and systems into complex forms, and then discusses several initial boundary value problems and Cauchy problems for quasilinear and nonlinear parabolic complex equations of second order with smooth coefficients or measurable coefficients. Parabolic complex equations are discussed in the nonlinear case and the boundary conditions usually include the initial irregular oblique derivative. The boundary value problems are considered in multiply connected domains and several methods are used.

Author : Watson
Publisher : Routledge
Page : 312 pages
File Size : 44,9 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781351425902

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Parabolic Equations on an Infinite Strip by Watson Pdf

This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.

Author : A. Asanov,E. R. Atamanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 53,7 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110900149

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Nonclassical and Inverse Problems for Pseudoparabolic Equations by A. Asanov,E. R. Atamanov Pdf

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.

Author : Tadeĭ Ivanovich Zeleni︠a︡k,M. Mikhail Mikhailovich Lavrentev,Michail Petrovič Višnevskij
Publisher : VSP
Page : 432 pages
File Size : 55,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9067642363

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Qualitative theory of parabolic equations. 1 by Tadeĭ Ivanovich Zeleni︠a︡k,M. Mikhail Mikhailovich Lavrentev,Michail Petrovič Višnevskij Pdf

In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.

Author : Zhi-Zhong Sun,Qifeng Zhang,Guang-hua Gao
Publisher : Walter de Gruyter GmbH & Co KG
Page : 432 pages
File Size : 50,9 Mb
Release : 2023-05-08
Category : Mathematics
ISBN : 9783110796018

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Finite Difference Methods for Nonlinear Evolution Equations by Zhi-Zhong Sun,Qifeng Zhang,Guang-hua Gao Pdf

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.

Author : Gary M. Lieberman
Publisher : World Scientific
Page : 472 pages
File Size : 52,8 Mb
Release : 1996
Category : Mathematics
ISBN : 981022883X

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Second Order Parabolic Differential Equations by Gary M. Lieberman Pdf

Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.

Author : Habib Ammari,Bryn Davies
Publisher : Walter de Gruyter GmbH & Co KG
Page : 122 pages
File Size : 53,9 Mb
Release : 2023-11-06
Category : Mathematics
ISBN : 9783110784961

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Metamaterial Analysis and Design by Habib Ammari,Bryn Davies Pdf

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.

Author : Roland Glowinski,Tsorng-Whay Pan
Publisher : Walter de Gruyter GmbH & Co KG
Page : 232 pages
File Size : 40,5 Mb
Release : 2022-09-19
Category : Mathematics
ISBN : 9783110785012

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Numerical Simulation of Incompressible Viscous Flow by Roland Glowinski,Tsorng-Whay Pan Pdf

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.

Author : Bruno Després
Publisher : Walter de Gruyter GmbH & Co KG
Page : 174 pages
File Size : 52,8 Mb
Release : 2022-08-22
Category : Mathematics
ISBN : 9783110783186

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Neural Networks and Numerical Analysis by Bruno Després Pdf

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.

Author : Victor A. Galaktionov
Publisher : CRC Press
Page : 384 pages
File Size : 46,5 Mb
Release : 2004-05-24
Category : Mathematics
ISBN : 9780203998069

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Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by Victor A. Galaktionov Pdf

Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un

Author : D. W. Burton
Publisher : Unknown
Page : 60 pages
File Size : 52,6 Mb
Release : 1957
Category : Differential equations, Parabolic
ISBN : UOM:39015094996413

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Explicit Numerical Solution of Parabolic Differential Equations by D. W. Burton Pdf

Author : P. G. Danilaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 128 pages
File Size : 50,8 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940916

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Coefficient Inverse Problems for Parabolic Type Equations and Their Application by P. G. Danilaev Pdf

As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monograph the author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.

Author : Alessandra Lunardi
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 40,7 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034805575

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Analytic Semigroups and Optimal Regularity in Parabolic Problems by Alessandra Lunardi Pdf

The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)