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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 1 4
Second-Order Linear PDEs:
Classification, Problems,
and Pa rticular Solutions
14.1 Classification of Second-Order Linear Partial
Differential Equations
14.1.1 Equations with Two Independent Variables
Examples of equations encountered in applications.
Three basic types of partial differential equations are distinguished—parabolic, hyper-
bolic, and elliptic. The solutions of the equations pertaining to each of the types have
their own characteristic qualitative differences.
The simplest example of a parabolic equation is the heat equation
∂w
∂t
2
w
∂x
2
= 0, (14.1.1.1)
where the variables t and x play the role of time and the spatial coordinate,
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Publisher Resources

ISBN: 9781466581494