Theory and Modern Applications
Table 1 The effect of the damping terms
From: Blowup for semilinear wave equation with space-dependent damping and combined nonlinearities
Range of β | Damping term | |
|---|---|---|
\(\frac{\mu}{(1+t)^{\beta}}u_{t}\) | \(\frac{\mu}{(1+|x|)^{\beta}}u_{t}\) | |
(−∞,−1) | Overdamping | Effective |
[−1,1) | Effective | |
1 | Scaling invariant | Scaling invariant |
(1,+∞) | Scattering | Scattering |