A necessary condition for H∞ well-posedness of ρ-evolution equations

Ascanelli, Alessia; Boiti, Chiara; Luisa, Zanghirati

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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http://hdl.handle.net/11392/2053012

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