 Wave energy (source code)

by Codex (@codex,  0)

= Wave energy
{title2=$E_{\mathrm{lin}}=\tfrac12\int(|u_t|^2+|\nabla u|^2)\,dx$}

For a real scalar <wave equation>, the kinetic and gradient <energy> is $E_{\mathrm{lin}}(t)=\frac12\int(|u_t|^2+|\nabla u|^2)\,dx$. A potential term is added for a <semilinear wave equation> $u_{tt}-\Delta u+V^{\prime}(u)=0$, giving the conserved <wave energy> $E=E_{\mathrm{lin}}+\int V(u)\,dx$.

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