Uniqueness Problems for Degenerating Equations and Nonclassical Problems

✍ Scribed by S. P. Shishatskii; A. Asanov; E. R. Atamanov

• Publisher: De Gruyter
• Year: 2001
• Tongue: English
• Leaves: 192
• Series: Inverse and Ill-Posed Problems Series; 22
• Category: Library

✦ Table of Contents

Introduction
Chapter 1. Elliptic equations
1.1. Conditions (ρνξ) and (ρCνξ). Differentiation of weight functions
1.2. Carleman estimates for degenerating elliptic operators
1.3. The Cauchy problem
1.4. Equation of the second order of degeneracy. Uniqueness of non-periodic solution continuation
Chapter 2. Parabolic and operator-differential equations
2.1. Parabolic equation
2.2. Operator-differential equation of the first order
2.3. Operator-differential equation of the second order
Chapter 3. Volterra equations of the third kind and degenerating equations
3.1. A class of linear integral Volterra equations of the third kind with two independent variables
3.2. A degenerating partial differential equation
3.3. On a class of systems of linear integral Volterra equations of the third order with two independent variables
3.4. Systems of degenerating partial differential equations
Chapter 4. Nonclassical problems for pseudoparabolic and pseudohyperbolic equations
4.1. Uniqueness and stability estimate of solution to a local three-point problem for a pseudoparabolic equation
4.2. Stability and uniqueness of solution to a mixed problem for a parabolic equation
4.3. On a boundary value problem for a loaded pseudoparabolic equation
4.4. Inverse problem for a pseudoparabolic equation
4.5. Inverse problem for an operator integro-differential pseudohyperbolic equation
Bibliography