| Abstract: |
| The present talk is concerned to the semilinear wave equation subject to a supercritical (resp. subcritical) growth with a nonlinear locally distributed damping on a smooth bounded domain growing sub-critically (resp. critically). We first construct approximate solutions using the truncation process and we show that approximate solutions decay uniformly in the phase space topology by using microlocal analysis tools and a unique continuation property. Then, we prove the global existence as well as the uniform decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively. The distinctive feature of the work is the truncation approach, which makes the analysis easier to apply when compared with the previous literature, by considering the well known Strichartz estimates as well as a unique continuation in the truncated process and recovering the desired uniform decay rate estimates in the limit process. |
|