NON-EXISTENCE OF GLOBAL WEAK SOLUTIONS TO SEMI-LINEAR WAVE EQUATIONS INVOLVING TIME-DEPENDENT STRUCTURAL DAMPING TERMS

We consider a semilinear wave equation involving a time-dependent structural damping term of the form¹ (Formula presented). Our results show the influence of the parameters β, σ on the nonexistence of global weak solutions under assumptions on the given system data. Our approach is based on the nonlinear capacity method combined with a pointwise estimate of the fractional Laplacian of some test functions, which was derived by Fujiwara (2018) (see also Fino and Dao (2022)). We extend the blowu-p results developed recently by Fino and Hamza (2022).