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Semilinear wave equation

Defocusing semilinear wave equation

Radial reduction of the three-dimensional wave equation

For $q=w_t+w_r$ and a radial weight $\psi$,
$$
\frac d{dt}\int_0^\infty\psi\left(\frac12q^2+\frac{|w|^{p+1}}{(p+1)r^{p-1}}\right)dr
=-\frac12\int_0^\infty\psi'q^2dr
+\frac1{p+1}\int_0^\infty\frac{|w|^{p+1}}{r^{p-1}}
\left(\psi'-(p-1)\frac\psi r\right)dr.
$$


Outgoing-energy identity for a radial defocusing wave

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 6 / Solution

Outgoing-energy identity for a radial defocusing wave

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Outgoing-energy identity for a radial defocusing wave

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