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Differential Equations Lecture Work Solutions 176

# Differential Equations Lecture Work Solutions 176 - 6...

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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. x u xx + u yy = x 2 b. x 2 u xx 2 xy u xy + y 2 u yy = e x c. e x u xx + e y u yy = u d. u xx + u xy xu yy = 0 in the left half plane ( x 0) e. x 2 u xx + 2 xyu xy + y 2 u yy + xyu x + y 2 u y = 0 f. u xx + xu yy = 0 (Tricomi equation) 2. Classify each of the following constant coeﬃcient equations a. 4 u xx + 5 u xy + u yy + u x + u
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• Fall '08
• BELL,D
• Partial differential equation, left half plane, Order PDEs, Constant Coefficient Equations, linear second order, uyy + ux

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