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Re: NDSolve system of partial eqn
 To: mathgroup at smc.vnet.net
 Subject: [mg66396] Re: NDSolve system of partial eqn
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Thu, 11 May 2006 02:15:59 0400 (EDT)
 Organization: Uni Leipzig
 References: <e3sh0g$lu0$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Hi,
you have the solution for \[Phi][z,t]
but you ask NDSolve[] to find it and
NDSolve[] don't like this, eliminate \[Phi][z,t]
and it should work
Regards
Jens
"Peter Breitfeld" <phbrf at tonline.de> schrieb im
Newsbeitrag news:e3sh0g$lu0$1 at smc.vnet.net...

 I want to solve the following system of partial
deqns .

 \[Mu] = 0.01;
 \[Gamma] = 0.03;
 \[Rho] = 1000;
 Subscript[\[Delta], \[Epsilon]] = 0.171;
 K = 0.008;
 g = 9.81;
 Subscript[k, \[Alpha]] = 1.52;

 Subscript[L, 0] = 0.0003;
 Subscript[D, eff] = 3.7/10^9;
 Subscript[\[Epsilon], 0] = 0.1;
 H = 1;
 Subscript[t, max] = 1000;

 eqn1 = D[\[Epsilon][z, t], t] + D[\[Phi][z, t],
z] == 0;
 eqn2 = \[Phi][z, t] == (K*L[z,
t]^2*\[Epsilon][z, t]^(3/2)*(\[Rho]*g +
 Subscript[\[Delta],
\[Epsilon]]^(1/2)*\[Gamma]* D[1/(L[z, t]*
 \[Epsilon][z, t]^(1/2)),
 z]))/\[Mu];

 eqn4 = D[L[z, t], t] == Subscript[D, eff]* ((1 
Subscript[k, \[Alpha]]*
 \[Epsilon][z, t]^(1/2))^2/ L[z, t]);

 NDSolve[{eqn1, eqn2, eqn4,
 \[Epsilon][z, 0] == Subscript[\[Epsilon], 0],
 L[z, 0] == Subscript[L, 0],
 \[Phi][H, t] == 0,
 \[Phi][0, t] == 0},
 {\[Epsilon], \[Phi], L}, {z, H, 0},
 {t, 0, 1}]

 Trying to solve this, I get the Error
"NDSolv::ivone", but I don't
 really understand what I did wrong. Can someone
please explain it to me?

 Gruss Peter
 

============================================
 Peter Breitfeld, Bad Saulgau, Germany 
http://www.pBreitfeld.de

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