This paper corrects Asakura's observation on semilinear wave equations with non-compactly supported data by showing a sharp blow-up theorem for classical solutions. We know that there is no global in time solution for any power nonlinearity if the spatial decay of the initial data is weak, in spite of finite propagation speed of the linear wave. Our theorem clarifes the final criterion on such a phenomenon.
|Number of pages||7|
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 2011 Sept|
- Semilinear wave equations