Uniqueness Problems for Degenerating Equations and Nonclassical Problems
1st Edition
Published on 26. March 2001
Book
Hardback
183 pages
978-90-6764-341-2 (ISBN)
Description
01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
The study of Cauchy problems for degenerating equations and systems is a wide and actively developing area. However, the majority deals mainly with Cauchy problems for hyperbolic equations and systems and characteristic Cauchy problems for parabolic equations and systems.
This volume in the Inverse and Ill-Posed Problems Series presents the results that were obtained on uniqueness for the main (ill-posed in the regular case) Cauchy problems for equations of the second order with exponential degeneracy. The Cauchy problem for a degenerating elliptic equation, the noncharacteristic Cauchy problem, and the mixed problem with reversed time for a degenerating parabolic equation are considered. Stability estimates that guarantee conditional well-posedness of the considered Cauchy problems in terms of the inverse problems theory are given, along with uniqueness theorems.
The study of Cauchy problems for degenerating equations and systems is a wide and actively developing area. However, the majority deals mainly with Cauchy problems for hyperbolic equations and systems and characteristic Cauchy problems for parabolic equations and systems.
This volume in the Inverse and Ill-Posed Problems Series presents the results that were obtained on uniqueness for the main (ill-posed in the regular case) Cauchy problems for equations of the second order with exponential degeneracy. The Cauchy problem for a degenerating elliptic equation, the noncharacteristic Cauchy problem, and the mixed problem with reversed time for a degenerating parabolic equation are considered. Stability estimates that guarantee conditional well-posedness of the considered Cauchy problems in terms of the inverse problems theory are given, along with uniqueness theorems.
More details
Series
Language
English
Place of publication
Zeist
Netherlands
Publishing group
Brill
Target group
College/higher education
Professional and scholarly
US School Grade: College Graduate Student
Weight
440 gr
ISBN-13
978-90-6764-341-2 (9789067643412)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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S. P. Shishatskii | A. Asanov | E. R. Atamanov
Uniqueness Problems for Degenerating Equations and Nonclassical Problems
Book
02/2015
1st Edition
De Gruyter
€269.00
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S. P. Shishatskii | A. Asanov | E. R. Atamanov
Uniqueness Problems for Degenerating Equations and Nonclassical Problems
E-Book
10/2014
1st Edition
De Gruyter
€179.95
Available for download
S. P. Shishatskii | A. Asanov | E. R. Atamanov
Uniqueness Problems for Degenerating Equations and Nonclassical Problems
Book
03/2001
1st Edition
De Gruyter
€189.95
Shipment within 7-9 days
Content
Introduction
Chapter 1. Elliptic equations
Conditions (??? and ?c?? Differentiation of weight functions
Carleman estimates for degenerating ellipting operators
The Cauchy problem
Equations of the second order of degeneracy. Uniqueness of non-periodic solution continuation
Chapter 2. Parabolic and operator-differential equations
Parabolic equation
Operator-differential equation of the first order
Operator-differential equation of the second order
Chapter 3. Volterra equations of the third kind and degenerating equations
A class of linear integral Volterra equations of the third kind with two independent variables
A degenerating partial differential equation
On a class of systems of linear integral Volterra equations of the third order with two independent variables
Systems of degenerating partial differential equations
Chapter 4. Nonclassical problems for pseudoparabolic and pseudohyperbolic equations
Uniqueness and stability estimate of solution to a local three-point problem for a pseudoparabolic equation
Stability and uniqueness of solution to a mixed problem for a parabolic equation
On a boundary value problem for a loaded pseudoparabolic equation
Inverse problem for a pseudoparabolic equation
Inverse problem for an operator integro-differential pseudohyperbolic equation
Bibliography
Chapter 1. Elliptic equations
Conditions (??? and ?c?? Differentiation of weight functions
Carleman estimates for degenerating ellipting operators
The Cauchy problem
Equations of the second order of degeneracy. Uniqueness of non-periodic solution continuation
Chapter 2. Parabolic and operator-differential equations
Parabolic equation
Operator-differential equation of the first order
Operator-differential equation of the second order
Chapter 3. Volterra equations of the third kind and degenerating equations
A class of linear integral Volterra equations of the third kind with two independent variables
A degenerating partial differential equation
On a class of systems of linear integral Volterra equations of the third order with two independent variables
Systems of degenerating partial differential equations
Chapter 4. Nonclassical problems for pseudoparabolic and pseudohyperbolic equations
Uniqueness and stability estimate of solution to a local three-point problem for a pseudoparabolic equation
Stability and uniqueness of solution to a mixed problem for a parabolic equation
On a boundary value problem for a loaded pseudoparabolic equation
Inverse problem for a pseudoparabolic equation
Inverse problem for an operator integro-differential pseudohyperbolic equation
Bibliography