Author: G. AngerPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112480287
Category : Social Science
Languages : en
Pages : 300
Book Description
Inverse and Improperly Posed Problems in Differential Equations
Author: G. AngerPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112480287
Category : Social Science
Languages : en
Pages : 300
Book Description
Improperly Posed Problems in Partial Differential Equations
Author: L. E. PaynePublisher: SIAM
ISBN: 9781611970463
Category : Mathematics
Languages : en
Pages : 81
Book Description
Improperly posed Cauchy problems are the primary topics in this discussion which assumes that the geometry and coefficients of the equations are known precisely. Appropriate references are made to other classes of improperly posed problems. The contents include straight forward examples of methods eigenfunction, quasireversibility, logarithmic convexity, Lagrange identity, and weighted energy used in treating improperly posed Cauchy problems. The Cauchy problem for a class of second order operator equations is examined as is the question of determining explicit stability inequalities for solving the Cauchy problem for elliptic equations. Among other things, an example with improperly posed perturbed and unperturbed problems is discussed and concavity methods are used to investigate finite escape time for classes of operator equations.
Some Improperly Posed Problems of Mathematical Physics
Author: Michail M. LavrentievPublisher: Springer Science & Business Media
ISBN: 3642882102
Category : Science
Languages : en
Pages : 115
Book Description
This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif ferential equation from a certain family of its solutions. Novosibirsk June, 1967 M. M. LAVRENTIEV Table of Contents Chapter I Formu1ation of some Improperly Posed Problems of Mathematic:al Physics § 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . § 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 § 2 The Cauchy Problem for the Laplace Equation . . . . . . . 18 § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity. . . . . . . . . . . . . 22 § 4 Analytic Continuation of a Function of Two Real Variables 32 § 5 Analytic Continuation of Harmonic Functions from a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter III Inverse Problems for Differential Equations § 1 The Inverse Problem for a Newtonian Potential . . . . . . .
Inverse Problems in Partial Differential Equations
Author: David L. ColtonPublisher: SIAM
ISBN: 9780898712520
Category : Mathematics
Languages : en
Pages : 234
Book Description
Some Improperly Posed Problems of Mathematical Physics
Author: Robert J. SackerNon-Standard and Improperly Posed Problems
Author: William F. AmesPublisher: Elsevier
ISBN: 008053774X
Category : Mathematics
Languages : en
Pages : 319
Book Description
Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary. The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration. Provides the first unified survey of the advances made in the last 15 years in the field Includes an up-to-date compendium of the mathematical literature on these topics
Inverse Problems in Differential Equations
Author: G. AngerPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112707176
Category : Mathematics
Languages : en
Pages : 256
Book Description
No detailed description available for "Inverse Problems in Differential Equations".
Inverse and Ill-posed Problems
Author: Heinz W. EnglPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 592
Book Description
Inverse and Ill-Posed Problems.
Inverse Problems for Partial Differential Equations
Author: Yurii Ya. BelovPublisher: Walter de Gruyter
ISBN: 3110944634
Category : Mathematics
Languages : en
Pages : 220
Book Description
This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.
Methods for Solving Incorrectly Posed Problems
Author: V.A. MorozovPublisher: Springer Science & Business Media
ISBN: 1461252806
Category : Mathematics
Languages : en
Pages : 275
Book Description
Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.