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Unformatted text preview: 6 Classiﬁcation and Characteristics 6.1 Physical Classiﬁcation 6.2 Classiﬁcation of Linear Second Order PDEs Problems
1. Classify each of the following as hyperbolic, parabolic or elliptic at every point (x, y ) of
f. x uxx + uyy = x2
x2 uxx − 2xy uxy + y 2uyy = ex
ex uxx + ey uyy = u
uxx + uxy − xuyy = 0 in the left half plane (x ≤ 0)
x2 uxx + 2xyuxy + y 2 uyy + xyux + y 2 uy = 0
uxx + xuyy = 0 (Tricomi equation) 2. Classify each of the following constant coeﬃcient equations
f. 4uxx + 5uxy + uyy + ux + uy = 2
uxx + uxy + uyy + ux = 0
3uxx + 10uxy + 3uyy = 0
uxx + 2uxy + 3uyy + 4ux + 5uy + u = ex
2uxx − 4uxy + 2uyy + 3u = 0
uxx + 5uxy + 4uyy + 7uy = sin x 3. Use any symbolic manipulator (e.g. MACSYMA or MATHEMATICA) to prove (6.1.19).
This means that a transformation does NOT change the type of the PDE. 176 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
- Fall '08