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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
Chapter 9
Second-Order
Elliptic Equations
with Two Space Variables
9.1 Laplace Equation
2
w = 0
The Laplace equation is often encountered in heat and mass transfer theory, fluid mechan-
ics, elasticity, electrostatics, and other areas of mechanics and physics. For example, in
heat and mass transfer theory, this equation describes steady-state temperature distribution
in the absence of heat sources and sinks in the domain under study.
A regular solution of the Laplace equation is called a harmonic function. The first
boundary value problem for the Laplace equation is often referred to as the D irichlet prob-
lem, and the second boundary value problem as
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Publisher Resources

ISBN: 9781466581494