A note on the classifications of hyperbolic and elliptic equations with polynomial coefficients.

*(English)*Zbl 1173.35404Summary: We consider the hyperbolic and elliptic partial differential equations with constant coefficients; then by using double convolutions we produce new equations with polynomial coefficients and classify the new equations. It is shown that the classifications of hyperbolic and elliptic equations with non-constant coefficients are similar to those of the original equations; that is, the equations are invariant under double convolutions.

##### MSC:

35E20 | General theory of PDEs and systems of PDEs with constant coefficients |

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\textit{A. Kılıçman} and \textit{H. Eltayeb}, Appl. Math. Lett. 21, No. 11, 1124--1128 (2008; Zbl 1173.35404)

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##### References:

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