Search results for " 35L70"
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Uniqueness and stability of an inverse problem for a semi-linear wave equation
2020
We consider the recovery of a potential associated with a semi-linear wave equation on $\mathbb{R}^{n+1}$, $n\geq 1$. We show a H\"older stability estimate for the recovery of an unknown potential $a$ of the wave equation $\square u +a u^m=0$ from its Dirichlet-to-Neumann map. We show that an unknown potential $a(x,t)$, supported in $\Omega\times[t_1,t_2]$, of the wave equation $\square u +a u^m=0$ can be recovered in a H\"older stable way from the map $u|_{\partial \Omega\times [0,T]}\mapsto \langle\psi,\partial_\nu u|_{\partial \Omega\times [0,T]}\rangle_{L^2(\partial \Omega\times [0,T])}$. This data is equivalent to the inner product of the Dirichlet-to-Neumann map with a measurement fun…
Blow-up of the non-equivariant 2+1 dimensional wave map
2014
It has been known for a long time that the equivariant 2+1 wave map into the 2-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit violations of equivariance.