$\begin{array}{cc}\multicolumn{1}{c}{\frac{\partial u}{\partial t}\hspace{0.5em}-\hspace{0.5em}\nabla \xb7({D}_{u}\hspace{0.5em}\nabla u)\hspace{0.5em}\hspace{0.5em}=\hspace{0.5em}\hspace{0.5em}0,\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}\frac{\partial w}{\partial t}\hspace{0.5em}-\hspace{0.5em}\nabla \xb7({D}_{w}\hspace{0.5em}\nabla w)\hspace{0.5em}\hspace{0.5em}=\hspace{0.5em}\hspace{0.5em}0,\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}\text{in}\Omega ,\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{for}t0,}& \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}(1)\end{array}$ |
$\begin{array}{cccc}\multicolumn{1}{c}{-\hspace{0.5em}{D}_{u}\frac{\partial u}{\partial z}}& =\hfill & \eta [\hspace{0.5em}\pm \hspace{0.5em}({C}_{\mathrm{min}}+{C}_{1}\hspace{0.5em}{f}_{1}(w))\mp \hspace{0.5em}{C}_{2}\hspace{0.5em}\hspace{0.5em}u]+{\delta}_{j}\hspace{0.5em}{C}_{0}\hspace{0.5em}P\hspace{0.5em}u\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{on}\hspace{0.5em}\hspace{0.5em}{F}_{j}^{\pm},\hspace{0.5em}\hspace{0.5em}j=1,\dots ,N,\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}t>0,\hfill & \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}(2)\\ \multicolumn{1}{c}{-\hspace{0.5em}{D}_{w}\frac{\partial w}{\partial r}}& =\hfill & {g}_{1}(w)\hspace{0.5em}-\hspace{0.5em}C\hspace{0.5em}{g}_{2}(u)\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{on}\hspace{0.5em}\hspace{0.5em}{\partial}_{o}\Omega ,\hspace{0.5em}\hspace{0.5em}t>0,\hfill & \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}(3)\end{array}$ |
${f}_{1}(w)=\frac{1}{1+(\gamma w{)}^{{m}_{\mathrm{Ca}}}}\hspace{0.5em},\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}{g}_{1}(w)=\frac{w}{1+w}\hspace{0.5em},\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}{g}_{2}(u)=\frac{{u}^{{m}_{\mathrm{cG}}}}{1+{u}^{{m}_{\mathrm{cG}}}}\hspace{0.5em},$ | $(4)$ |
$J={J}_{\mathrm{cG}}+{J}_{\mathrm{ex}}\hspace{0.5em},\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{with}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}{J}_{\mathrm{cG}}={j}_{\mathrm{cG}}^{max}{g}_{2}(u)\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{and}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}{J}_{\mathrm{ex}}={j}_{\mathrm{ex}}^{\mathrm{sat}}{g}_{1}(w)\hspace{0.5em},$ | $(5)$ |
$P(t)=\frac{1}{2}\hspace{0.5em}{\text{E}}^{*}(t)/{A}_{\mathrm{activ}}$ | $(6)$ |
${\text{E}}^{*}(t)=\Phi \xb7\left(\frac{{\nu}_{\mathrm{RE}}}{{k}_{R}-{k}_{E}}\right)({e}^{-{k}_{E}t}-{e}^{-{k}_{R}t}),\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>0\hspace{0.5em},$ | $(7)$ |
Fig.1a Figure 1a |
Fig.1b
Figure 1b |
Fig.2a Fig.2a |
Fig.2b Fig.2b |
*0.5!
Fig.3a Fig.3a | *0.5!
Fig.3a Fig.3b |
ACKNOWLEDGEMENTS |