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The Cauchy Problem in Kinetic Theory

The Cauchy Problem in Kinetic Theory PDF Author: Robert T. Glassey
Publisher: SIAM
ISBN: 0898713676
Category : Science
Languages : en
Pages : 246

Book Description
Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.

The Cauchy Problem in Kinetic Theory

The Cauchy Problem in Kinetic Theory PDF Author: Robert T. Glassey
Publisher: SIAM
ISBN: 0898713676
Category : Science
Languages : en
Pages : 246

Book Description
Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.

On the Cauchy Problem

On the Cauchy Problem PDF Author: Sigeru Mizohata
Publisher: Academic Press
ISBN: 148326906X
Category : Mathematics
Languages : en
Pages : 186

Book Description
Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.

Lectures on Cauchy's Problem in Linear Partial Differential Equations

Lectures on Cauchy's Problem in Linear Partial Differential Equations PDF Author: Jacques Hadamard
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 336

Book Description


Abstract Cauchy Problems

Abstract Cauchy Problems PDF Author: Irina V. Melnikova
Publisher: CRC Press
ISBN: 1420035495
Category : Mathematics
Languages : en
Pages : 259

Book Description
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat

The Cauchy Problem in General Relativity

The Cauchy Problem in General Relativity PDF Author: Hans Ringström
Publisher: European Mathematical Society
ISBN: 9783037190531
Category : Mathematics
Languages : en
Pages : 310

Book Description
The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaitre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those without prior background in the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.

Vector-valued Laplace Transforms and Cauchy Problems

Vector-valued Laplace Transforms and Cauchy Problems PDF Author: Wolfgang Arendt
Publisher: Springer Science & Business Media
ISBN: 3034850751
Category : Mathematics
Languages : en
Pages : 526

Book Description
Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .

Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics

Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics PDF Author: V.I. Shalashilin
Publisher: Springer Science & Business Media
ISBN: 9781402015427
Category : Mathematics
Languages : en
Pages : 246

Book Description
The optimal continuation parameter provides the best conditions in a linearized system of equations at any moment of the continuation process. This is one of the first books in which the best parametrization is regarded systematically for a wide class of problems. It is of interest to scientists, specialists, and postgraduate students of applied and numerical mathematics and mechanics.

Stochastic Cauchy Problems in Infinite Dimensions

Stochastic Cauchy Problems in Infinite Dimensions PDF Author: Irina V. Melnikova
Publisher: CRC Press
ISBN: 1498785859
Category : Mathematics
Languages : en
Pages : 160

Book Description
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

The Cauchy Problem

The Cauchy Problem PDF Author: Hector O. Fattorini
Publisher: Cambridge University Press
ISBN: 0521302382
Category : Mathematics
Languages : en
Pages : 664

Book Description
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.

The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations

The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations PDF Author: J. C. Meyer
Publisher: Cambridge University Press
ISBN: 1107477395
Category : Mathematics
Languages : en
Pages : 177

Book Description
A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.