A remark on a critical exponent for the semilinear dissipative wave equation in the one dimensional half space.
The author proves the existence and uniqueness of a solution to the half space mixed problem for the equation \(u_{tt}-u_{xx}+u_{t}=| u| ^{p}\) for small initial data. A new lower bound of the power \(p\) of the nonlinear term and better decay estimates of the solution are obtained.
scientific article; zbMATH DE number 2004922