# Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case

## TL;DR

This paper investigates the blow-up behavior of solutions to a weakly coupled system of semilinear damped wave equations of derivative type, establishing blow-up results in subcritical and critical cases using functional analysis and iteration methods.

## Contribution

It extends blow-up analysis to damped wave systems with derivative nonlinearities, identifying the critical curve matching undamped systems.

## Key findings

- Blow-up occurs in the subcritical case.
- Critical curve matches that of undamped systems.
- Uses Kato's lemma and slicing method for proofs.

## Abstract

In this paper we consider the blow-up for solutions to a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the corresponding single semilinear equation, we employ Kato's lemma to derive the blow-up result in the subcritical case. On the other hand, in the critical case an iteration procedure based on the slicing method is employed. Let us point out that we find as critical curve in the p-q plane for the pair of exponents (p, q) in the nonlinear terms the same one as for the weakly coupled system of semilinear not-damped wave equations with the same kind of nonlinearities.