Scattering in the Energy Space for Boussinesq Equations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-07

AUTHORS

Claudio Muñoz, Felipe Poblete, Juan C. Pozo

ABSTRACT

In this note we show that all small solutions in the energy space of the generalized 1D Boussinesq equation must decay to zero as time tends to infinity, strongly on slightly proper subsets of the space-time light cone. Our result does not require any assumption on the power of the nonlinearity, working even for the supercritical range of scattering. For the proof, we use two new Virial identities in the spirit of works (Kowalczyk et al. in J Am Math Soc 30:769–798, 2017; Kowalczyk et al. in Lett Math Phys 107(5):921–931, 2017). No parity assumption on the initial data is needed. More... »

PAGES

127-141

References to SciGraph publications

  • 1999-03. Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations in INVENTIONES MATHEMATICAE
  • 2001-04. Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1993-07. Instability of solitary waves for generalized Boussinesq equations in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 1988-03. Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1982-09. Stability theory for solitary-wave solutions of scalar field equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2005-09. A Remark on Asymptotic Completeness for the Critical Nonlinear Klein-Gordon Equation in LETTERS IN MATHEMATICAL PHYSICS
  • 2017-05. Nonexistence of small, odd breathers for a class of nonlinear wave equations in LETTERS IN MATHEMATICAL PHYSICS
  • 2013-11. Nonlinear Stability of MKdV Breathers in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00220-018-3099-7

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    http://dx.doi.org/10.1007/s00220-018-3099-7

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