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6.4.2: Singularidad

( \newcommand{\kernel}{\mathrm{null}\,}\)

Las soluciones suficientemente regulares del problema del valor de límite inicial (6.4.1) - (6.4.3) se determinan de manera única ya que a partir de

\ begin {eqnarray*}
C_t&=&D\ triángulo c\\\ mbox {in}\\ Omega\ times (0,\ infty)\\
c (x,0) &=&0\\
\ frac {\ parcial c} {\ parcial n} &=& 0\\\ mbox {on}\\ parcial\ Omega\ times (0,\ infty).
\ end {eqnarray*}
se deduce que para cada\tau>0
\ begin {eqnarray*}
0&=&\ int_0^\ tau\\ int_\ Omega\\ left (C_tc-D (\ triángulo c) c\ derecha)\ dxdt\\
&=&\ int_\ Omega\\ int_0^\ tau\\ frac {1} {2}\ frac {parcial} {\ parcial t} (c^2)\ dtdx+ D\ int_\ Omega\\ int_0^\ tau\ |\ nabla_xc|^2\ dxdt\\
&=&\ frac {1} {2} {2}\ int_\ Omega\ c^2 (x,\ tau)\ dx+D\ int_\ Omega\\ int_0^\ tau\ |\ nabla_xc|^2\ dxdt.
\ end {eqnarray*}


This page titled 6.4.2: Singularidad is shared under a not declared license and was authored, remixed, and/or curated by Erich Miersemann.

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