A decay estimate for a class of hyperbolic pseudo-differential equations

Lucente, Sandra, and Ziliotti, Guido. "A decay estimate for a class of hyperbolic pseudo-differential equations." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.3 (1999): 173-190. <http://eudml.org/doc/252442>.

@article{Lucente1999,
abstract = {We consider the equation \( u\_\{t\} − i \Lambda u = 0 \), where \( \Lambda = \lambda(D\_\{x\}) \) is a first order pseudo-differential operator with real symbol \( \lambda (\xi) \). Under a suitable convexity assumption on \( \lambda \) we find the decay properties for \( u(t,x) \). These can be applied to the linear Maxwell system in anisotropic media and to the nonlinear Cauchy Problem \( u\_\{t\} − i \Lambda u = f (u) \), \( u(0,x) = g(x) \). If \( f(u) \) is a smooth function which satisfies \( f(u) \simeq |u|^\{p\} \) near \( u = 0 \), and \( g \) is small in suitably Sobolev norm, we prove global existence theorems provided \( p \) is greater than a critical exponent.},
author = {Lucente, Sandra, Ziliotti, Guido},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Decay estimate; Nonlinear hyperbolic equations; Small data; decay estimate; nonlinear hyperbolic equation; small data; Maxwell system in anisotropic media; nonlinear Cauchy problem},
language = {eng},
month = {9},
number = {3},
pages = {173-190},
publisher = {Accademia Nazionale dei Lincei},
title = {A decay estimate for a class of hyperbolic pseudo-differential equations},
url = {http://eudml.org/doc/252442},
volume = {10},
year = {1999},
}

TY - JOUR
AU - Lucente, Sandra
AU - Ziliotti, Guido
TI - A decay estimate for a class of hyperbolic pseudo-differential equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/9//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 3
SP - 173
EP - 190
AB - We consider the equation \( u_{t} − i \Lambda u = 0 \), where \( \Lambda = \lambda(D_{x}) \) is a first order pseudo-differential operator with real symbol \( \lambda (\xi) \). Under a suitable convexity assumption on \( \lambda \) we find the decay properties for \( u(t,x) \). These can be applied to the linear Maxwell system in anisotropic media and to the nonlinear Cauchy Problem \( u_{t} − i \Lambda u = f (u) \), \( u(0,x) = g(x) \). If \( f(u) \) is a smooth function which satisfies \( f(u) \simeq |u|^{p} \) near \( u = 0 \), and \( g \) is small in suitably Sobolev norm, we prove global existence theorems provided \( p \) is greater than a critical exponent.
LA - eng
KW - Decay estimate; Nonlinear hyperbolic equations; Small data; decay estimate; nonlinear hyperbolic equation; small data; Maxwell system in anisotropic media; nonlinear Cauchy problem
UR - http://eudml.org/doc/252442
ER -