In the hyperbolic Cauchy problem, the well-posedness in Sobolev spaces is strictly related to the modulus of continuity of the coefficients. This holds true for p-evolution equations with real characteristics (p=1 hyperbolic equations, p=2 vibrating plate and Schrödinger type models, …). We show that, for p≥2 a lack of regularity in t can be balanced by a damping of the too fast oscillations as the space variable x→∞. This cannot happen in the hyperbolic case p=1 because of the finite speed of propagation.

M. Cicognani, F. Colombini (2013). A well-posed Cauchy problem for an evolution equation with coefficients of low regularity. JOURNAL OF DIFFERENTIAL EQUATIONS, 254, 3573-3595 [10.1016/j.jde.2013.01.033].

A well-posed Cauchy problem for an evolution equation with coefficients of low regularity

CICOGNANI, MASSIMO;
2013

Abstract

In the hyperbolic Cauchy problem, the well-posedness in Sobolev spaces is strictly related to the modulus of continuity of the coefficients. This holds true for p-evolution equations with real characteristics (p=1 hyperbolic equations, p=2 vibrating plate and Schrödinger type models, …). We show that, for p≥2 a lack of regularity in t can be balanced by a damping of the too fast oscillations as the space variable x→∞. This cannot happen in the hyperbolic case p=1 because of the finite speed of propagation.
2013
M. Cicognani, F. Colombini (2013). A well-posed Cauchy problem for an evolution equation with coefficients of low regularity. JOURNAL OF DIFFERENTIAL EQUATIONS, 254, 3573-3595 [10.1016/j.jde.2013.01.033].
M. Cicognani; F. Colombini
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/133983
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact