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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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marked as duplicate by Hans Lundmark, user91500, jvdhooft, Sahiba Arora, kingW3 Jul 11 '17 at 17:09

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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 Jul 11 '17 at 11:32
  • $\begingroup$ In book shepley L. Ross they explained it with digrams $\endgroup$ – Pranita Gupta Jul 11 '17 at 11:47

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