Blow up of Solutions for a Coupled Kirchhoff-type Equations with Degenerate Damping Terms

In this paper, we investigate a system of coupled Kirchhoff-type equations with degenerate damping terms. We prove a nonexistence of global solutions with positive initial energy. Later, we give some estimates for lower bound of the blow up time

On the Cauchy problem for a weakly coupled system of semi-linear σ\sigma-evolution equations with double dissipation

In this paper, we would like to consider the Cauchy problem for a multi-component weakly coupled system of semi-linear $\sigma$-evolution equations with double dissipation for any $\sigma\ge 1$. The first main purpose is to obtain the global (in time) existence of small data solutions in the supercritical condition by assuming additional $L^1$ regularity for the initial data and using multi-loss of decay wisely. For the second main one, we are interested in establishing the blow-up results together with sharp estimates for lifespan of solutions in the subcritical case. The proof is based on a contradiction argument with the help of modified test functions to derive the upper bound estimates. Finally, we succeed in catching the lower bound estimate by constructing Sobolev spaces with the time-dependent weighted functions of polynomial type in their corresponding norms.Comment: 19 page