A note on existence of global classical solutions to nonlinear wave equations
The author examines the semilinear wave equation \[ u_{tt}-\Delta u=t^{1-k}u\quad k,\quad x\in {\mathbb{R}}\quad 3,\quad t>0 \] with data \(u(x,0)=0\), \(u_ t(x,0)=g(x).\) For g(x) satisfying a growth condition related to the Lane-Emden equation of index \(k\geq 5\) and with g(x) smooth and positive, it is shown that there exists a classical global unique solution.
scientific article; zbMATH DE number 4063673
scientific article