Convergence of exterior solutions to radial Cauchy solutions for $\partial_t^2U-c^2\Delta U=0$
Consider the Cauchy problem for the 3-D linear wave equation $\partial_t^2U-c^2\Delta U=0$ with radial initial data $U(0,x)=\Phi(x)=\varphi(|x|)$, $U_t(0,x)=\Psi(x)=\psi(|x|)$. A standard result states that $U$ belongs to $C([0,T];H^s(\mathbb{R}^3))$ whenever $(\Phi,\Psi)\in H^s\times H^{s-1}(\...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/266/abstr.html |