We consider p-evolution equations, for p ≥ 2, 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| → +∞.
Data di pubblicazione: | 2016 | |
Titolo: | A necessary condition for H∞ well-posedness of ρ-evolution equations | |
Autori: | Ascanelli, Alessia; Boiti, Chiara; Luisa, Zanghirati | |
Rivista: | ADVANCES IN DIFFERENTIAL EQUATIONS | |
Keywords: | p-evolution equations, well-posedness in Sobolev spaces, pseudo-differential operators | |
Abstract in inglese: | We consider p-evolution equations, for p ≥ 2, 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| → +∞. | |
Handle: | http://hdl.handle.net/11392/2053012 | |
Appare nelle tipologie: | 03.1 Articolo su rivista |
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