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