Question: System of quasilinear PDEs

Hello,

I am trying to solve the following system of quasilinear PDEs for dependent variables pA(z,t), pB(z,t), pC(z,t) using Maple 14:

> system:= [

.15e-3*diff(pA(z,t),t)+.83e-1*diff(pA(z,t),z)+.47e-3/(1+.11e-6*pA(z,t)+.14e-4*pB(z,t)+.73e-4*pC(z,t))^2*((1+.14e-4*pB(z,t)+.73e-4*pC(z,t))*diff(pA(z,t),t)-.14e-4*pA(z,t)*diff(pB(z,t),t)-.73e-4*pA(z,t)*diff(pC(z,t),t)) = 0,

.15e-3*diff(pB(z,t),t)+.83e-1*diff(pB(z,t),z)+.90e-1/(1+.11e-6*pA(z,t)+.14e-4*pB(z,t)+.73e-4*pC(z,t))^2*((1+.11e-6*pA(z,t)+.73e-4*pC(z,t))*diff(pB(z,t),t)-.11e-6*pB(z,t)*diff(pA(z,t),t)-.73e-4*pB(z,t)*diff(pC(z,t),t)) = 0,

.15e-3*diff(pC(z,t),t)+.83e-1*diff(pC(z,t),z)+10./(1+.11e-6*pA(z,t)+.14e-4*pB(z,t)+.73e-4*pC(z,t))^2*((1+.11e-6*pA(z,t)+.14e-4*pB(z,t))*diff(pC(z,t),t)-.11e-6*pC(z,t)*diff(pA(z,t),t)-.14e-4*pC(z,t)*diff(pB(z,t),t)) = 0

];

Initial and boundary conditions are:

> ibc:= [pA(z,0) = 0, pB(z,0) = 0, pC(z,0) = 0, pA(0,t) = .67e7, pB(0,t) = .14e6, pC(0,t) = .14e6];

When I ask for a solution

> pdsolve(sys,ibc,[pA,pB,pC],numeric,time=t,range=0..1);

I get 'Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence'.

Is it because in each PDE in the system there are derivatives of more than one dependent variable wrt time? If so, why is Maple not able to solve such a system?

Thanks in advance.

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