Consider the one dimensional heat equation Əu = Ôrau, x E R, t > 0. xx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 1. Consider the one dimensional heat equation
x E R, t > 0.
(1.1)
We say that u is a classical solution if u e C2((0, ∞) × R) and satisfies the heat equation for every
x ER and t > 0.
(1) Verify that (1.1) it is a linear PDE and determine the order of the equation.
(2) Verify that the functions
1
u1(t, x) = t+ *
1
u2(t, x) =
V4nt
:e
4t
are classical solutions to the heat equation.
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