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Asymptotic Behavior of Solutions of the Dispersion Generalized Benjamin–Ono Equation

Linares, F. ; Mendez, A. ; Ponce, G.

Journal of dynamics and differential equations, 2021-06, Vol.33 (2), p.971-984 [Periódico revisado por pares]

New York: Springer US

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  • Título:
    Asymptotic Behavior of Solutions of the Dispersion Generalized Benjamin–Ono Equation
  • Autor: Linares, F. ; Mendez, A. ; Ponce, G.
  • Assuntos: Applications of Mathematics ; Asymptotic properties ; Breathers ; Commutators ; Convergence ; Dispersion ; Infimum ; Infinity ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations ; Solitary waves
  • É parte de: Journal of dynamics and differential equations, 2021-06, Vol.33 (2), p.971-984
  • Descrição: We show that for any uniformly bounded in time H 1 ∩ L 1 solution of the dispersion generalized Benjamin–Ono equation, the limit infimum, as time t goes to infinity, converges to zero locally in an increasing-in-time region of space of order t / log t . This result is in accordance with the one established by Muñoz and Ponce (Proc Am Math Soc 147(12):5303–5312, 2019) for solutions of the Benjamin–Ono equation. Similar to solutions of the Benjamin–Ono equation, for a solution of the dispersion generalized Benjamin–Ono equation, with a mild L 1 -norm growth in time, its limit infimum must converge to zero, as time goes to infinity, locally in an increasing on time region of space of order depending on the rate of growth of its L 1 -norm. As a consequence, the existence of breathers or any other solution for the dispersion generalized Benjamin–Ono equation moving with a speed “slower” than a soliton is discarded. In our analysis the use of commutators expansions is essential.
  • Editor: New York: Springer US
  • Idioma: Inglês
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