deletions | additions       diff --git a/paragraph_2_Mimic_the_derivation__.tex b/paragraph_2_Mimic_the_derivation__.tex  index 2857655..bc40422 100644  --- a/paragraph_2_Mimic_the_derivation__.tex  +++ b/paragraph_2_Mimic_the_derivation__.tex 
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Combinding the divergence Theoreom with the fact that v has compact support and v(x,0) = 0 we have,  $$\iint_{-\Omega} \phi_{t}u + \phi_{x}f(u) dxdt = \iint_{-\Omega} [u_{t} + f(u)_{x}]\phi dxdt + \int_{x} \vareplison \int_{x = \varepsilon  (t)} [u^{-} \phiv_{2} \phi v_{2}  + f(u^{-}\phiv_{1}]ds$$ f(u^{-}\phi v_{1}]ds$$