### A Necessary condition for $H^\infty$ well-posedness of $p$-evolution equations

#### Abstract

We consider $p$-evolution equations, for $p\geq2$, with complex valued coefficients. We prove that a necessary condition for $H^\infty$ well-posedness of the associated Cauchy problem is that the imaginary part of the coefficient of the subprincipal part (in the sense of Petrowski) satisfies a decay estimate as $|x|\to+\infty$.

#### Article information

Source
Adv. Differential Equations Volume 21, Number 11/12 (2016), 1165-1196.

Dates
First available in Project Euclid: 13 October 2016

Ascanelli, Alessia; Boiti, Chiara; Zanghirati, Luisa. A Necessary condition for $H^\infty$ well-posedness of $p$-evolution equations. Adv. Differential Equations 21 (2016), no. 11/12, 1165--1196. https://projecteuclid.org/euclid.ade/1476369299.