| Abstract: |
| Consider the initial-boundary value problem for the two-dimensional semilinear damped wave equation with the critical nonlinearity
$u_{tt} - \Delta u + u_t = u^2$
in the exterior of the unit ball in $\mathbb{R}^2$ with the Dirichlet boundary condition.
We obtain a sharp double-exponential type lifespan estimate
$T(\verepsilon) \geq \exp(\exp(C \varepsilon^{-1}))$
under the assumption of radial symmetry.
To achieve this result, we introduce a new technique to control an $L^1$-type norm and a new Gagliardo-Nirenberg type estimate with logarithmic weight. |
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