Infinite propagation speed of a weakly dissipative modified two-component Dullin-Gottwald-Holm system

Abstract We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.

[1]  Min Zhu,et al.  On the wave-breaking phenomena for the periodic two-component Dullin–Gottwald–Holm system , 2012 .

[2]  Darryl D. Holm,et al.  Singular solutions of a modified two-component Camassa-Holm equation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Darryl D. Holm,et al.  An integrable shallow water equation with peaked solitons. , 1993, Physical review letters.

[4]  E. Ott,et al.  Damping of Solitary Waves , 1970 .

[5]  E. Novruzov Blow-up of solutions for the dissipative Dullin–Gottwald–Holm equation with arbitrary coefficients , 2016 .

[6]  Shou-Fu Tian,et al.  Asymptotic behavior of a weakly dissipative modified two-component Dullin-Gottwald-Holm system , 2018, Appl. Math. Lett..

[7]  D. H. Sattinger,et al.  Acoustic Scattering and the Extended Korteweg– de Vries Hierarchy , 1998, solv-int/9901007.

[8]  Rossen I. Ivanov,et al.  Shallow Water Waves , 2019, Theoretical and Mathematical Physics.

[9]  A. Constantin,et al.  The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations , 2007, 0709.0905.

[10]  Lixin Tian,et al.  On the Well-Posedness Problem and the Scattering Problem for the Dullin-Gottwald-Holm Equation , 2005 .

[11]  J. Escher,et al.  Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation , 1998 .

[12]  Existence and Uniqueness of Low Regularity Solutions for the Dullin-Gottwald-Holm Equation , 2006 .

[13]  Yue Liu,et al.  On the wave‐breaking phenomena for the two‐component Dullin–Gottwald–Holm system , 2012, J. Lond. Math. Soc..