second order parabolic differential equations

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Second Order Parabolic Differential Equations

Author : Gary M. Lieberman
ISBN : 981022883X
Genre : Mathematics
File Size : 57. 21 MB
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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.

Second Order Parabolic Differential Equations

Author : G M Lieberman
ISBN : 9789814498111
Genre : Mathematics
File Size : 84. 90 MB
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This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear boundary conditions by means of a priori estimates. The first seven chapters give a description of the linear theory and are suitable for a graduate course on partial differential equations. The last eight chapters cover the nonlinear theory for smooth solutions. They include much of the author's research and are aimed at researchers in the field. A unique feature is the emphasis on time-varying domains. Contents:IntroductionMaximum PrinciplesIntroduction to the Theory of Weak SolutionsHölder EstimatesExistence, Uniqueness, and Regularity of SolutionsFurther Theory of Weak SolutionsStrong SolutionsFixed Point Theorems and Their ApplicationsComparison and Maximum PrinciplesBoundary Gradient EstimatesGlobal and Local Gradient BoundsHölder Gradient Estimates and Existence TheoremsThe Oblique Derivative Problem for Quasilinear Parabolic EquationsFully Nonlinear Equations I. IntroductionFully Nonlinear Equations II. Hessian Equations Readership: Graduate students and researchers in mathematics. keywords:Partial Differential Equations;A Priori Estimates;Initial-Boundary Value Problems;Maximum Principle;Existence;Uniqueness;Regularity;Linear Boundary Conditions;Nonlinear Boundary Conditions “In the reviewer's opinion the author of this nicely written book has succeeded very well in his goal that ‘this book was to create a companion volume to Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S Trudinger’.” Mathematical Reviews “The book provides an essentially self-contained exposition of the theory of second order parabolic partial differential equations.” Mathematics Abstracts

Author : Gary M. Lieberman
ISBN : 7506259605
Genre : Differential equations, Parabolic
File Size : 55. 76 MB
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Second Order Equations Of Elliptic And Parabolic Type

Author : E. M. Landis
ISBN : 0821897810
Genre :
File Size : 58. 33 MB
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Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.

Nonlinear Partial Differential Equations Of Second Order

Author : Guangchang Dong
ISBN : 0821845543
Genre : Mathematics
File Size : 66. 70 MB
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Addresses a class of equations central to many areas of mathematics and its applications. This book addresses a general approach that consists of the following: choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution.

Partial Differential Equations Of Parabolic Type

Author : Avner Friedman
ISBN : 9780486318264
Genre : Mathematics
File Size : 43. 69 MB
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With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Finite Difference Methods In Financial Engineering

Author : Daniel J. Duffy
ISBN : 9781118856482
Genre : Business & Economics
File Size : 72. 7 MB
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The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

Second Order Partial Differential Equations In Hilbert Spaces

Author : Giuseppe Da Prato
ISBN : 1139433431
Genre : Mathematics
File Size : 45. 68 MB
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Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.

Green Functions For Second Order Parabolic Integro Differential Problems

Author : Maria Giovanna Garroni
ISBN : UOM:39015029224147
Genre : Mathematics
File Size : 38. 34 MB
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Second Order Linear Differential Equations In Banach Spaces

Author : H.O. Fattorini
ISBN : 0080872190
Genre : Mathematics
File Size : 59. 66 MB
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Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

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