Boundary Value Problems For Transport Equations

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Boundary Value Problems For Transport Equations

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Author : Valeri Agoshkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Boundary Value Problems For Transport Equations written by Valeri Agoshkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].

Boundary Value Problems For Transport Equations

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Author : Valeri Agoshkov
language : en
Publisher:
Release Date : 1998-09-29

Boundary Value Problems For Transport Equations written by Valeri Agoshkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-29 with categories.

Boundary Value Problems In Abstract Kinetic Theory

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Author : W. Greenberg
language : en
Publisher: Birkhäuser
Release Date : 2013-12-14

Boundary Value Problems In Abstract Kinetic Theory written by W. Greenberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Social Science categories.

This monograph is intended to be a reasonably self -contained and fairly complete exposition of rigorous results in abstract kinetic theory. Throughout, abstract kinetic equations refer to (an abstract formulation of) equations which describe transport of particles, momentum, energy, or, indeed, any transportable physical quantity. These include the equations of traditional (neutron) transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. The mathematical problems addressed within the monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The reader is assumed to have a certain familiarity with elementary aspects of functional analysis, especially basic semigroup theory, and an effort is made to outline any more specialized topics as they are introduced. Over the past several years there has been substantial progress in developing an abstract mathematical framework for treating linear transport problems. The benefits of such an abstract theory are twofold: (i) a mathematically rigorous basis has been established for a variety of problems which were traditionally treated by somewhat heuristic distribution theory methods; and (ii) the results obtained are applicable to a great variety of disparate kinetic processes. Thus, numerous different systems of integrodifferential equations which model a variety of kinetic processes are themselves modelled by an abstract operator equation on a Hilbert (or Banach) space.

Handbook Of Differential Equations Stationary Partial Differential Equations

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Author : Michel Chipot
language : en
Publisher: Elsevier
Release Date : 2011-08-11

Handbook Of Differential Equations Stationary Partial Differential Equations written by Michel Chipot and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.

This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems.* Collection of self-contained, state-of-the-art surveys* Written by well-known experts in the field* Informs and updates on all the latest developments

Compressible Navier Stokes Equations

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Author : Pavel Plotnikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-04

Compressible Navier Stokes Equations written by Pavel Plotnikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-04 with Mathematics categories.

The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.

Mathematical Models Of Non Linear Excitations Transfer Dynamics And Control In Condensed Systems And Other Media

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Author : Ludmilla A. Uvarova
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematical Models Of Non Linear Excitations Transfer Dynamics And Control In Condensed Systems And Other Media written by Ludmilla A. Uvarova and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The articles in this book are derived from the Third International Conference of the same name, held June 29-July 3, 1998. Topics include: nonlinear exaltations in condensed systems, evolution of complex systems, dynamics and structure of molecular and biomolecular systems, mathematical models of transfer processes in nonlinear systems and numerical modeling and algorithms.

Hyperbolic Problems Theory Numerics Applications

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Author : Michael Fey
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Hyperbolic Problems Theory Numerics Applications written by Michael Fey and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

[Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations

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Author : Pham Loi Vu
language : en
Publisher: CRC Press
Release Date : 2019-11-11

Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations written by Pham Loi Vu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features • The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. • Solving the associated initial value problem or initial-boundary value problem for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the time-dependent scattering data (SD) are constructed from the initial and boundary conditions. • The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. • Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM.

A Collection Of Problems On The Equations Of Mathematical Physics

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Author : Vasilij S. Vladimirov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09

A Collection Of Problems On The Equations Of Mathematical Physics written by Vasilij S. Vladimirov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Science categories.

The extensive application of modern mathematical teehniques to theoretical and mathematical physics requires a fresh approach to the course of equations of mathematical physics. This is especially true with regards to such a fundamental concept as the 80lution of a boundary value problem. The concept of a generalized solution considerably broadens the field of problems and enables solving from a unified position the most interesting problems that cannot be solved by applying elassical methods. To this end two new courses have been written at the Department of Higher Mathematics at the Moscow Physics anrl Technology Institute, namely, "Equations of Mathematical Physics" by V. S. Vladimirov and "Partial Differential Equations" by V. P. Mikhailov (both books have been translated into English by Mir Publishers, the first in 1984 and the second in 1978). The present collection of problems is based on these courses and amplifies them considerably. Besides the classical boundary value problems, we have ineluded a large number of boundary value problems that have only generalized solutions. Solution of these requires using the methods and results of various branches of modern analysis. For this reason we have ineluded problems in Lebesgue in tegration, problems involving function spaces (especially spaces of generalized differentiable functions) and generalized functions (with Fourier and Laplace transforms), and integral equations.

Geometric And Computational Spectral Theory

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Author : Alexandre Girouard
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-10-30

Geometric And Computational Spectral Theory written by Alexandre Girouard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Mathematics categories.

A co-publication of the AMS and Centre de Recherches Mathématiques The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Séminaire de Mathématiques Supérieures on Geometric and Computational Spectral Theory, held from June 15–26, 2015, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.