Question: Non-linear PDE problem

Hey everyone. The last few days I work on a non-linear PDE. 

U*`∂`(F(s))/`∂`(x) = -k*sigma*cos(theta)*`∂`(F(s)*kro(s)*`∂`(J(s))/`∂`(x))/(`μo`*sqrt(k/phi)*`∂`(x));

with boundary conditions: when x=-∞: s=swi       and  

x=L : U*dF(s)+k*sigma*F(s)*kro(s)*`∂`(J(s))/(`μo`*sqrt(k/phi)*`∂`(x))

I need to plot s over x ,  whare  swi<s<1-sor   and 0<x<L

I have writen the following equations that calculate all parameters of the PDE.

> restart;  
 
> krowi := 1; krwor := .1; aw := 1.16; ao := 3.69; alpha := 0.6e-1; U := 2.9374109836-10^(-7); L := 0.552566e-1; m := .5; sor := .3; swi := .25; k := 10^(-14); `μw` := 0.1e-2; `μo` := 0.5e-2; sigma := 0.72e-1; phi := .3; theta := 0;
> C := krowi*(1-sor-swi)^(-ao);
 
> A := krwor*(1-sor-swi)^(-aw);
 
> krw(s):=A*(s-swi)^(aw):
 
> kro(s):=C*(1-sor-s)^(ao):
 
> F(s):=((krw(s))/(muw))/((krw(s))/(muw)+(kro(s))/(muo)):
 
> J(s):=alpha[((s-swi)/(1-sor-swi))^(-1/(m))-1]^(1-m):
 
> PDE:=U*`∂`(F(s))/`∂`(x) = -k*sigma*cos(theta)*`∂`(F(s)*kro(s)*`∂`(J(s))/`∂`(x))/(`μo`*sqrt(k/phi)*`∂`(x));

When I try different methos, most time I get this message:

Error, (in pdsolve/info) first argument is not a differential equation

Any suggestions?

Thank you