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Consider the PDE

P(x,y)2ux2+ex2ey22uxy+Q(x,y)2uy2+e2xux+eyuy=0

where P and Q are polynomials in two variables with real coefficients. Then which of the following is true for all choices of P and Q ?

1. There exists R>0 such that the PDE is elliptic in {(x,y)R2:x2+y2>R}

2. There exists R>0 such that the PDE is hyperbolic in {(x,y)R2:x2+y2>R}

3. There exists R>0 such that the PDE is parabolic in {(x,y)R2:x2+y2>R}

4. There exists R>0 such that the PDE is hyperbolic in {(x,y)R2:x2+y2<R}
in Differential Equation by Expert | 319 views

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