A note on the lifespan of solutions to the semilinear wave equation with weighted nonlinearity

We investigate the lifespan of solutions to a specific variant of the semilinear wave equation, which incorporates weighted nonlinearity u_tt-u_xx =|x|^α |u|^p, (t,x)∈ (0,∞)×ℝ, where p>1, α∈ℝ. We explore the behavior of solutions for small initial data, considering the influence of weighted nonlinearities on the lifespan.