Consider the following initial value problem 0 if x <-1 Ut + 3uu, = 0, u(x,0) = 1 otherwise. 1 if x < 1 . и + Зии, — 0, и(х,0) - otherwise. Explain which problem admits a solution consisting of a shock wave, and which one admits a solution in the form of a rarefaction wave. Give a graphical construction of the solutions using characteristics.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following initial value problem
if x < -1
• Ut + 3uug = 0, u(x,0) =
1
otherwise.
1
if x < 1
. и + Зиид — 0, и(х,0)
otherwise.
Explain which problem admits a solution consisting of a shock wave, and which one
admits a solution in the form of a rarefaction wave. Give a graphical construction of
the solutions using characteristics.
Transcribed Image Text:Consider the following initial value problem if x < -1 • Ut + 3uug = 0, u(x,0) = 1 otherwise. 1 if x < 1 . и + Зиид — 0, и(х,0) otherwise. Explain which problem admits a solution consisting of a shock wave, and which one admits a solution in the form of a rarefaction wave. Give a graphical construction of the solutions using characteristics.
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