This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum.

Coclite, G.M., Gargano, F., & Sciacca, V. (2012). Analytic Solutions and Singularity Formation for the Peakon b-Family Equations. ACTA APPLICANDAE MATHEMATICAE, 122(1), 419-434 [10.1007/s10440-012-9753-8].

Analytic Solutions and Singularity Formation for the Peakon b-Family Equations

GARGANO, Francesco;SCIACCA, Vincenzo
2012

Abstract

This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum.
Settore MAT/07 - Fisica Matematica
Coclite, G.M., Gargano, F., & Sciacca, V. (2012). Analytic Solutions and Singularity Formation for the Peakon b-Family Equations. ACTA APPLICANDAE MATHEMATICAE, 122(1), 419-434 [10.1007/s10440-012-9753-8].
File in questo prodotto:
File Dimensione Formato  
Cocl_Garg_Sciac.pdf

Solo gestori archvio

Dimensione 1.01 MB
Formato Adobe PDF
1.01 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/10447/73764
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 17
social impact