Geodesic
On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 267-279
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In this paper, we study the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. We first establish the local well-posedness for the weakly dissipative μ-Hunter–Saxton equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.

DOI : 10.1016/j.anihpc.2013.02.008
Classification : 35Q35, 35G25, 58D05
Keywords: A weakly dissipative μ-Hunter–Saxton, Blow-up scenario, Blow-up, Strong solutions, Global existence 
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     author = {Liu, Jingjing and Yin, Zhaoyang},
     title = {On the {Cauchy} problem of a weakly dissipative {\protect\emph{\ensuremath{\mu}}-Hunter{\textendash}Saxton} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {267--279},
     year = {2014},
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Liu, Jingjing; Yin, Zhaoyang. On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 267-279. doi: 10.1016/j.anihpc.2013.02.008

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