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

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.