How to solve a system of PDAEs with eigenvalue

[ktsharp]

I have the following system of partial differential algebraic equations:

[ tex ] \frac{1}{H_p}\frac{\partial H_p}{\partial t} = - \frac{\partial W_p}{\partial x} - \frac{f1(H_p,c_p,W_p)}{H_p}, [ \tex ]
[tex]\frac{1}{H_p}\frac{\partial}{\partial t}(H_p c_p} = - \frac{\partial}{\partial x}(W_p c_p) - \frac{f2(H_p,W_p,c_p)}{H_p}, [\tex]<br /> $$0 = f2(H_p,c_p,W_p) + f3(H_p,c_p,W_p). [\tex]<br /> <br /> with the following conditions:<br /> Hp(x,0) = 5<br /> Wp(x,0) = s1(x)<br /> cp(x,0) = s2(x)<br /> <br /> Hp(0,t) = s3(t)<br /> Wp(0,t) = W0<br /> Wp(L,t) = 0<br /> d(cp)/dx (L,t) = 0<br /> <br /> How can I solve this numerically?$$[/tex]

 

[tiny-tim]

type "/tex" not "\tex" (or "$$") …

I have the following system of partial differential algebraic equations:

$$\frac{1}{H_p}\frac{\partial H_p}{\partial t} = - \frac{\partial W_p}{\partial x} - \frac{f1(H_p,c_p,W_p)}{H_p},$$
$$\frac{1}{H_p}\frac{\partial}{\partial t}(H_p c_p) = - \frac{\partial}{\partial x}(W_p c_p) - \frac{f2(H_p,W_p,c_p)}{H_p},$$
$$0 = f2(H_p,c_p,W_p) + f3(H_p,c_p,W_p).$$

 

[ktsharp]

[UPDATED]

I have the following system of partial differential algebraic equations:

$$\frac{1}{H}\frac{\partial H}{\partial t} = - \frac{\partial W}{\partial x} - \frac{f_1(H,c,W)}{H},$$
$$\frac{1}{H}\frac{\partial}{\partial t}(H c) = - \frac{\partial}{\partial x}(W c) - \frac{f_2(H,W,c)}{H},$$
$$0 = f_2(H,c,W) + f_3(H,c,W).$$

with the following conditions:
H(x,0) = 5
W(x,0) = s1(x)
c(x,0) = s2(x)

H(0,t) = s3(t)
W(0,t) = W0
W(L,t) = 0
d(c)/dx (L,t) = 0

How can I solve this numerically?