The Cauchy problem for 𝑝-evolution equations

Cicognani, Massimo; Colombini, Ferruccio

doi:10.1090/S0002-9947-10-05171-8

The Cauchy problem for $p$-evolution equations
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by Massimo Cicognani and Ferruccio Colombini

Trans. Amer. Math. Soc. 362 (2010), 4853-4869

DOI: https://doi.org/10.1090/S0002-9947-10-05171-8

Published electronically: April 28, 2010

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Abstract:

In this paper we deal with the Cauchy problem for evolution equations with real characteristics. We show that the problem is well-posed in Sobolev spaces assuming a suitable decay of the coefficients as the space variable $x\to \infty$. In some cases, such a decay may also compensate a lack of regularity with respect to the time variable $t$.

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