Book contents
- Frontmatter
- Contents
- Editor's Statement
- Foreword by Felix E. Browder
- Preface
- Chapter 0 Preliminaries
- Chapter 1 Introduction
- Chapter 2 The Cauchy Problem
- Chapter 3 The Initial-Value Problem
- Chapter 4 The Initial-Boundary-Value Problem for the Quarter Plane with Temperature-Boundary Specification
- Chapter 5 The Initial-Boundary-Value Problem for the Quarter Plane with Heat-Flux-Boundary Specification
- Chapter 6 The Initial-Boundary-Value Problem for the Semi-Infinite Strip with Temperature-Boundary Specification and Heat-Flux-Boundary Specification
- Chapter 7 The Reduction of Some Initial-Boundary-Value Problems for the Semi-Infinite Strip, to Integral Equations: Some Exercises
- Chapter 8 Integral Equations
- Chapter 9 Solutions of Boundary-Value Problems for All Times and Periodic Solutions
- Chapter 10 Analyticity of Solutions
- Chapter 11 Continuous Dependence upon the Data for Some State-Estimation Problems
- Chapter 12 Some Numerical Methods for Some State-Estimation Problems
- Chapter 13 Determination of an Unknown Time-Dependent Diffusivity a(t) from Overspecified Data
- Chapter 14 Initial- and/or Boundary-Value Problems for General Regions with Hölder Continuous Boundaries
- Chapter 15 Some Properties of Solutions in General Domains
- Chapter 16 The Solution in a General Region with Temperature-Boundary Specification: The Method of Perron-Poincaré
- Chapter 17 The One-Phase Stefan Problem with Temperature-Boundary Specification
- Chapter 18 The One-Phase Stefan Problem with Flux-Boundary Specification: Some Exercises
- Chapter 19 The Inhomogeneous Heat Equation ut = uxx + f(x, t)
- Chapter 20 An Application of the Inhomogeneous Heat Equation: The Equation ut = uxx + F(x,t,u,ux)
- Some References to the Literature on ℒ(u) ≡ uxx – ut
- Symbol Index
- Subject Index
Chapter 20 - An Application of the Inhomogeneous Heat Equation: The Equation ut = uxx + F(x,t,u,ux)
Published online by Cambridge University Press: 05 February 2012
- Frontmatter
- Contents
- Editor's Statement
- Foreword by Felix E. Browder
- Preface
- Chapter 0 Preliminaries
- Chapter 1 Introduction
- Chapter 2 The Cauchy Problem
- Chapter 3 The Initial-Value Problem
- Chapter 4 The Initial-Boundary-Value Problem for the Quarter Plane with Temperature-Boundary Specification
- Chapter 5 The Initial-Boundary-Value Problem for the Quarter Plane with Heat-Flux-Boundary Specification
- Chapter 6 The Initial-Boundary-Value Problem for the Semi-Infinite Strip with Temperature-Boundary Specification and Heat-Flux-Boundary Specification
- Chapter 7 The Reduction of Some Initial-Boundary-Value Problems for the Semi-Infinite Strip, to Integral Equations: Some Exercises
- Chapter 8 Integral Equations
- Chapter 9 Solutions of Boundary-Value Problems for All Times and Periodic Solutions
- Chapter 10 Analyticity of Solutions
- Chapter 11 Continuous Dependence upon the Data for Some State-Estimation Problems
- Chapter 12 Some Numerical Methods for Some State-Estimation Problems
- Chapter 13 Determination of an Unknown Time-Dependent Diffusivity a(t) from Overspecified Data
- Chapter 14 Initial- and/or Boundary-Value Problems for General Regions with Hölder Continuous Boundaries
- Chapter 15 Some Properties of Solutions in General Domains
- Chapter 16 The Solution in a General Region with Temperature-Boundary Specification: The Method of Perron-Poincaré
- Chapter 17 The One-Phase Stefan Problem with Temperature-Boundary Specification
- Chapter 18 The One-Phase Stefan Problem with Flux-Boundary Specification: Some Exercises
- Chapter 19 The Inhomogeneous Heat Equation ut = uxx + f(x, t)
- Chapter 20 An Application of the Inhomogeneous Heat Equation: The Equation ut = uxx + F(x,t,u,ux)
- Some References to the Literature on ℒ(u) ≡ uxx – ut
- Symbol Index
- Subject Index
Summary
- Type
- Chapter
- Information
- The One-Dimensional Heat Equation , pp. 344 - 356Publisher: Cambridge University PressPrint publication year: 1984