The Cauchy problem for 𝑝-evolution equations

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 → ∞ x\to \infty . In some cases, such a decay may also compensate a lack of regularity with respect to the time variable t t .