NDSolve system of partial eqn

• To: mathgroup at smc.vnet.net
• Subject: [mg66349] NDSolve system of partial eqn
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Wed, 10 May 2006 06:34:18 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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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