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A note on the classifications of hyperbolic and elliptic equations with polynomial coefficients. (English) Zbl 1173.35404
Summary: 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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References:
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[2] Tyn Myint-U, Partial Differential Equations of Mathematical Physics, New York, 1980 · Zbl 0428.35001
[3] Christian Constanda, Solution Techniques for Elementary Partial Differential Equations, New York, 2002 · Zbl 1042.35001
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