A necessary condition for $H^\infty$ well-posedness of p-evolution equations
Analysis of PDEs
2016-10-25 v2
Abstract
We consider p-evolution equations, for , with complex valued coefficients. We prove that a necessary condition for 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 goes to infinity.
Cite
@article{arxiv.1406.6183,
title = {A necessary condition for $H^\infty$ well-posedness of p-evolution equations},
author = {A. Ascanelli and C. Boiti and L. Zanghirati},
journal= {arXiv preprint arXiv:1406.6183},
year = {2016}
}