Determine all solutions u = u(x1, x2) of du du (1 — и). + (1+u) dx1 = 1, dx2 X1, X2 E R, u(x1, x2) = 0, xi = x2. Nhere are the solutions defined? Interpret your results in the light of the general local existence theorem.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Partial Differential Equations

Determine all solutions u =
u(x1, x2) of
ди
+ (1+ u)
du
(1 – u):
1,
dx2
X1, x2 E R,
u(x1, x2)
0,
xi = x2.
Where are the solutions defined? Interpret your results in the light of the general local existence
theorem.
Transcribed Image Text:Determine all solutions u = u(x1, x2) of ди + (1+ u) du (1 – u): 1, dx2 X1, x2 E R, u(x1, x2) 0, xi = x2. Where are the solutions defined? Interpret your results in the light of the general local existence theorem.
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