Separation of Variables Heat flows along an infinite (in the y-direction) strip of width a (in the x-direction). Find the general solution u(x, y, t) to the two-dimensional heat equation ди - k√² u = 0 Ət subject to the boundary conditions: u(0, y, t) = 0 = u(a, y, t); — u(x, y, t) lim u(x, y, t) = 0. x+h = = 0; and |t=0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 15E
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Separation of Variables
Heat flows along an infinite (in the y-direction) strip of width a (in the x-direction).
Find the general solution u(x, y, t) to the two-dimensional heat equation
ди
- k√² u = 0
Ət
subject to the boundary conditions: u(0, y, t) = 0 = u(a, y, t); — u(x, y, t)
lim u(x, y, t) = 0.
x+h
=
= 0; and
|t=0
Transcribed Image Text:Separation of Variables Heat flows along an infinite (in the y-direction) strip of width a (in the x-direction). Find the general solution u(x, y, t) to the two-dimensional heat equation ди - k√² u = 0 Ət subject to the boundary conditions: u(0, y, t) = 0 = u(a, y, t); — u(x, y, t) lim u(x, y, t) = 0. x+h = = 0; and |t=0
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,