Critical exponent for semi-linear structurally damped wave equation of derivative type

Abstract

The main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: (Formula presented.) with μ>0, n ≥ 1, σ∈(0,2], and p>1. In particular, we would like to prove the nonexistence of global weak solutions by using a new test function and suitable sign assumptions on the initial data in both the subcritical case and the critical case.