Differential Equations Lecture Work Solutions 176

Differential Equations Lecture Work Solutions 176 - 6...

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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 the domain a. b. c. d. e. 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 a. b. c. d. e. 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.

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