Classification of PDEs v1

Classification of PDEs v1 - Notes by Ben Griffin 2-8 (in...

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Notes by Ben Griffin 1/7 2-8 (in White) Mathematical Character of the Basic Equations: Classification of PDE’s General form: xx xy yy ABC D   , where subscript denotes differentiation (e.g., 2 xy xy  ) A, B, …, D are all functions of   ,,, , yx but not of the second derivatives 2 nd order quasi-linear PDE From this point we can classify a PDE at a point P(x 0 , y 0 ), depending on the sign of the discriminant function 2 4 BA C this can vary as a function of x, y. An example of this would be linearized compressible flow analysis, 22 ˆˆ 2 10 M     . The Mach number can vary from subsonic to supersonic in transonic flow. This vastly changes the nature of the PDE.
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Notes by Ben Griffin 2/7 3 Classes 1. Hyperbolic: the PDE is hyperbolic at (x 0 , y 0 ) if 2 40 BA C usually deal with propagation problems, which are characterized by a second derivative with respect to time.
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Classification of PDEs v1 - Notes by Ben Griffin 2-8 (in...

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