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Unique Continuation Principles for Some Equations of Benjamin-Ono Type

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Nonlinear Equations: Methods, Models and Applications

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 54))

Abstract

By equations of Benjamin-Ono type we mean either

$${{\partial }_{t}}u(t) + \sigma Lu(t) + F(u(t)) = 0,$$
(1)

or

$${{\partial }_{t}}(u(t) + \sigma Lu(t)) + F(u(t)) = 0,$$
(2)

where Lis a linear (possibly unbounded) operator, F is (in general) a nonlinear function of its argument and v denotes the Hilbert transform

$$(\sigma f)(x) = p\upsilon \frac{1}{\pi }\int_{\mathbb{R}} {\frac{{f(y)}}{{y - x}}} dy.$$
(3)

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Author information

Authors and Affiliations

  1. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110 Jardim Botânico, Rio de Janeiro, RJ, Brazil, 22460-320

    Rafael José Iorio Jr.

Authors
  1. Rafael José Iorio Jr.
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy

    Daniela Lupo  & Carlo D. Pagani  & 

  2. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini, 50, 20133, Milano, Italy

    Bernhard Ruf

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Iorio, R.J. (2003). Unique Continuation Principles for Some Equations of Benjamin-Ono Type. In: Lupo, D., Pagani, C.D., Ruf, B. (eds) Nonlinear Equations: Methods, Models and Applications. Progress in Nonlinear Differential Equations and Their Applications, vol 54. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8087-9_12

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  • DOI: https://doi.org/10.1007/978-3-0348-8087-9_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9434-0

  • Online ISBN: 978-3-0348-8087-9

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