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Dayo Ogundipe edited paragraph_2_Mimic_the_derivation__.tex
over 8 years ago
Commit id: 957180aee77d497227d489bbf6bafb4ab41b8ed0
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Combinding the divergence Theoreom with the fact that v has compact support and v(x,0) = 0 we have,
$$\iint_{-\Omega} \phi_{t}u + \phi_{x}f(u) dxdt =
- \iint_{-\Omega} [u_{t} +
f(u)_{x}]\phi (f(u))_{x}]\phi dxdt + \int_{x = \varepsilon (t)} [u^{-} \phi v_{2} + f(u^{-}\phi v_{1}]ds$$