PDEMOC10

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If S_{1}\, and S_{2}\, are two graphs \left[S_{i}=u_{i}(x,y),i=1,2\right]\, that are integral surfaces of V=<a,b,c>\, and intersect in a curve \chi \,, show that \chi \, is a characteristic curve.


From this problem, we know that given any point on an integral surface, the surface contains the unique characteristic curve passing through that point.

So let p\in \chi \,. Then u_{1}\, contains the characteristic curve passing through p\, and so does u_{2}\,. Therefore p\in u_{1}\cap u_{2}\,. But u_{1}\cap u_{2}=\chi \,, so \chi \, is the characteristic curve passing through p\,.



Main Page : Partial Differential Equations : Method of Characteristics