Question: how i solve the coupled system of pde

Dear All,

This's my first post on this website; I'm hoping I can get some useful ideas on how to approach the numerical solution for system of PDE's, with initial and boundary conditions.  I'm using Maple 15.

The PDE is,

pde:={diff(p(r,t),r)-v(r,t)^2/r-g1=0,diff(v(r,t),r$2)+beta*diff(diff(v(r,t),r$2),t)-diff(v(r,t),r)*(1/r)-(beta/r)*diff(diff(v(r,t),r),t) +diff(v(r,t),t)*(beta/r^2)+v(r,t)/r^2+(2/r + C*diff(p(r,t),r))*(diff(v(r,t),r)-v(r,t)/r+beta*diff(diff(v(r,t),r),t)- 1/r * beta*diff(v(r,t),t)-Re*(1+lambda)*exp(1-p(r,t))*diff(v(r,t),t)-(1+lambda)*exp(1-p(r,t))*g2=0};

The initial and boundary conditions are,

IBC:={p(1,t)=k,v(r,0)=0,v(1,t)=sint,v(2,t)=0}

I'm trying to solve and plot,

sol:=pdsolve(pde,IBC,numeric,time=t,range=0..1)

but i'm getting an 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

Regards

J. Lee