How can I solve this PDE equation?

∂c/∂t+Q∂c/∂v=Ri

R1=∑_(i=D)^G▒KFiCf

R2=KFDCF-∑_(i=N)^G▒KDiCD

R3=KFNCF+KDNCD-KNGCN

R4=KFG+KDGCD+KNGCN

I.C.: Ci(v,0)=Cis

B.C.: Q(0,t)=Qin &Ci(0,t)=Ci0

[Walter Roberson]

Please also post an image of the equations. Your notation is not clear.

You seem to be using i as a subscript with D and G as scalars, a sum over variable i ranging from D to G. But then KDiCD would look to be K*Di*C*D for some unknown K and C, but that would imply that D should be subscripted.

In the definition of R1, you have Cf, and in some of the other places you have CF . Is that a mistake, that they should all be Cf ? Or is Cf a single variable and CF is C*F for some unknown C and F?

Please be clear as to what the parameters are of the system, what the different variable names are, and where the boundaries of the variable names are.

[saeed karami]

[saeed karami]

please see the second image

[Walter Roberson]

Sometimes you use i to subscript, like in R_f and R_D, but what is R_i in the first equation?

In assigning to R_D is that using D as a numeric value like it is used in the definition of R_f ? Or in the definitions of R_f and R_d are D and G and N abstract symbols in some sorted order but non-numeric order not stated here ?

[saeed karami]

In this question, all(D, N, NG, F, Fi, DG, FG, FD, FN and Di) are just symbols. For example, D is Just a symbol of R (Just for explain that factors) and don't has amount.

[Walter Roberson]

I do not know how to sum over a range of symbols unless the symbols have been ordered in some way. A summation over an unordered set of symbols is denoted by sigma variable_name element_of set; when you have sigma variable_name = value with upper value given, then it is assumed that the variables are orderable and vary by 1 -- e.g., i = N, i = N+1, i = N+2 ... i = G

Answer 1

[Pritesh Shah]

https://in.mathworks.com/help/matlab/math/partial-differential-equations.html

[saeed karami]

With thanks for your helping... Best,