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A sufficient condition for hyperbolicity of partial differential operators with constant coefficient principal part


Author: Joseph L. Dunn
Journal: Trans. Amer. Math. Soc. 201 (1975), 315-327
MSC: Primary 35L25
DOI: https://doi.org/10.1090/S0002-9947-1975-0355358-9
MathSciNet review: 0355358
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Abstract: Let $ P$ be a differential operator with principal part $ {P_m}$, and suppose that $ {P_m}$ has constant coefficients and is hyperbolic. It is shown that the condition for hyperbolicity of $ P$ when $ P$ has constant coefficients, namely, that $ P$ is weaker than $ {P_m}$ is also a sufficient condition for hyperbolicity in the case where $ P$ does not have constant coefficients. Some generalizations are also made to the case where $ P$ is a square matrix of differential operators.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0355358-9
Keywords: Hyperbolic partial differential equation, energy integral, principal part with constant coefficients
Article copyright: © Copyright 1975 American Mathematical Society

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