Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation

الملخص EN

We study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation.

We firstly establish the local well-posedness result.

Then we present a precise blow-up scenario.

Moreover, we obtain several blow-up results and the blow-up rate of strong solutions.

Finally, we consider the asymptotic behavior of solutions.