6. Solve the Cauchy problem Ut + xux = -tu, u(x,0) = = COS I.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4. On the domain 0<x<1, t>0, consider the problem
ut + Cux = 0,
0<x< 1, t > 0,
u(x, 0)= 0,
0<x< 1,
u(0, t) te , t> 0,
=
with c> 0. Find a formula for the solution, and sketch a graph of u(1, t) for t > 0 when c = 2.
6. Solve the Cauchy problem
ut + xux-tu,
u(x, 0)
= COS I.
Transcribed Image Text:4. On the domain 0<x<1, t>0, consider the problem ut + Cux = 0, 0<x< 1, t > 0, u(x, 0)= 0, 0<x< 1, u(0, t) te , t> 0, = with c> 0. Find a formula for the solution, and sketch a graph of u(1, t) for t > 0 when c = 2. 6. Solve the Cauchy problem ut + xux-tu, u(x, 0) = COS I.
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