4. Consider the initial value problem Ut + uux 0, t > 0, -0 < x < ∞ u(x, 0) exp(-x*) . Sketch the characteristic curves. Find the point (t4, x+) where the solution breaks down.
4. Consider the initial value problem Ut + uux 0, t > 0, -0 < x < ∞ u(x, 0) exp(-x*) . Sketch the characteristic curves. Find the point (t4, x+) where the solution breaks down.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. Consider the initial value problem
Ut + uux
0,
t> 0,
-00 < x < ∞
u(x, 0)
exp(-æ4) .
Sketch the characteristic curves. Find the point (t4, x+) where the solution breaks down.
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