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According to introductory texts on PDEs linear equations up to second order can be classified into three types:

  • ellyptic
  • parabolic
  • hyperbolic

Obviously, this corresponds to the three types of conic sections. But what is the intuition of this classification? How are conic sections and PDEs related?

To clarify: I do understand why classification makes sense. But why do we specifically use these three terms (e.g ellyptic, parabolic, hyperbolic).

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  • $\begingroup$ Perhaps also of interest: math.stackexchange.com/questions/21525/… $\endgroup$ Commented Jul 11, 2017 at 12:23
  • $\begingroup$ This answers the question. @Hans Also read your deleted answer - concise and helpful. $\endgroup$
    – Ben L
    Commented Jul 11, 2017 at 12:53

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There are only three possibilities for an equation that is greater than zero ,less then zero or equal to zero ..and each of them is related to one type of conic section.

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  • $\begingroup$ Indeed, but how exatly are they related? $\endgroup$
    – Ben L
    Commented Jul 11, 2017 at 11:32
  • $\begingroup$ In book shepley L. Ross they explained it with digrams $\endgroup$ Commented Jul 11, 2017 at 11:47

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