## Advances in Differential Equations

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

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

Alessia Ascanelli, Chiara Boiti, and Luisa Zanghirati

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1476369299

**Mathematical Reviews number (MathSciNet)**

MR3556763

**Zentralblatt MATH identifier**

1375.35090

**Subjects**

Primary: 35G10: Initial value problems for linear higher-order equations 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]

#### Citation

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