Question about the weak form


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8 weeks ago by
Nima  
Hi friends,

I have the following system of six equations:
   $-D_L\Delta L=-k_LrL$DLΔL=kLrL
   $-D_H\Delta H=-k_HrL$DHΔH=kHrL
   $-D_r\Delta r=r_0-r\left(k_HH+k_LL\right)$DrΔr=r0r(kHH+kLL)
   $-D_{Lox}\Delta L_{ox}=k_LrL-\lambda_{LoxM}ML_{ox}$DLoxΔLox=kLrLλLoxMMLox
   $-D_M\Delta M=-\nabla\cdot\left(M\chi_c\nabla P\right)+d_MM$DMΔM=·(MχcP)+dMM
   $-D_P\Delta P=\lambda_{PE}\frac{L_{ox}}{K_{L_{ox}}+L_{ox}}-d_pP$DPΔP=λPELoxKLox+Lox dpP

where L,H,M have Robin Boundary condition on a boundary marked by "1":
$\frac{\partial L}{\partial n}+\alpha_L\left(L-L_0\right)=0$Ln +αL(LL0)=0
$\frac{\partial H}{\partial n}+\alpha_H\left(H-H_0\right)=0$Hn +αH(HH0)=0
$\frac{\partial M}{\partial n}+\alpha_M\left(M-M_0\right)=0$Mn +αM(MM0)=0
While the others have zero Neumann BC on the boundary marked by "1". Also all six of them have zero Neumann BC on the boundary marked by "2". Here is what I have for the weak formulation.
F=k_L*r*L*v1*dx-D_L*alpha_L*(L_0-L)*v1*ds(1)+D_L*dot(grad(L),grad(v1))*dx\
 +k_H*r*H*v2*dx-D_H*alpha_H*(H_0-H)*v2*ds(1)+D_H*dot(grad(H),grad(v2))*dx\
 +r*(k_L*L+k_H*H)*v3*dx-r_0*v3*dx+D_r*dot(grad(r),grad(v3))*dx\
 +Lambda*M*Lox*v4*dx-k_L*r*L*v4*dx+D_Lox*dot(grad(Lox),grad(v4))*dx\
 + d_M*M*v5*dx-D_M*alpha_M*(M_0-M)*v5*ds(1)+D_M*dot(grad(M),grad(v5))*dx+ chi_c*M*dot(grad(P),grad(v5))*dx\
 + d_P*P*v6*dx-Lambda_PE*(Lox/(K_Lox+Lox))*v6*dx+Dp*dot(grad(P),grad(v6))*dx​
where v1,v2,v3,v4,v5,v6 are test functions. Is this form correct?

Thank you in advance
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