Global existence and blow-up for semilinear wave equations with variable coefficients
In this nice paper under review, the authors consider the critical exponent problem for the variable coefficients wave equation with a space dependent potential and source term. For sufficiently small data with compact support, if the power of nonlinearity is larger than the expected exponent, it is proved that there exists a global solution. In addition, the precise decay estimates for the energy, $L^2$ and $L^{p+1}$ norms of solutions are also established. Furthermore, the blow-up of the solutions is also proved for arbitrary initial data with compact support when the power of nonlinearity is less than some constant.
scientific article; zbMATH DE number 6979841