Chapter 1. The Diffusion Equation

  1. Richard Ghez

Published Online: 28 JAN 2005

DOI: 10.1002/3527602836.ch1

A Primer of Diffusion Problems

A Primer of Diffusion Problems

How to Cite

Ghez, R. (1988) The Diffusion Equation, in A Primer of Diffusion Problems, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527602836.ch1

Author Information

  1. IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 20 JUL 1988

ISBN Information

Print ISBN: 9780471846925

Online ISBN: 9783527602834

SEARCH

Keywords:

  • diffusion equation;
  • random walk;
  • continuum;
  • elementary properties;
  • conservation;
  • smoothing;
  • linearity;
  • invariance;
  • numerical methods;
  • heat conduction;
  • hydrodynamics;
  • quantum mechanics;
  • semiconductor equations;
  • conductors;
  • general balance laws

Summary

This chapter contains sections titled:

  • Isotropic One-dimensional Random Walk

  • Continuum Equations

  • Elementary Properties of the Diffusion Equation

    • A.1 Conservation in continuous regions

    • A.2 Conservation at fixed surfaces of discontinuity

    • A.3 Conservation at a moving boundary

    • B. Smoothing property

    • C.1 Linearity of the diffusion equation

    • C.2 Invariance under changes of scale and translations

  • Numerical Methods

  • A Numerical Example

  • Higher Dimensions and Coordinate Systems

  • Other Instances of the Diffusion Equation

    • A. Heat conduction

    • B. Hydrodynamics

    • C. Quantum mechanics

    • D. Semiconductor equations

    • E. Conductors

  • General Balance Laws and Constitutive Relations

  • References