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.
@article{AIHPC_2014__31_2_267_0, author = {Liu, Jingjing and Yin, Zhaoyang}, title = {On the Cauchy problem of a weakly dissipative $\mu$-Hunter--Saxton equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {31}, year = {2014}, pages = {267-279}, doi = {10.1016/j.anihpc.2013.02.008}, mrnumber = {3181669}, zbl = {1302.35320}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2014__31_2_267_0} }
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) pp. 267-279. doi : 10.1016/j.anihpc.2013.02.008. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_2_267_0/
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