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Question: How to solve PDEs system?

Question:How to solve PDEs system?

Lupita 10 Maple 18
pde pdsolve condition
October 20 2015
1

I am trying to solve system of partial differential equation, but i got some trouble. This is system of heat equations

Here are the equations:

restart;with(PDEtools):
U1 := diff_table(u1(x,t)):
pde[1] := (1/kappa1)*U1[t]=U1[x,x];

bc[1]:=u1(-L, t)=V;

 

U2 := diff_table(u2(x,t)):
pde[2] := (1/kappa2)*U2[t]=U2[x,x];

bc[2]:=u2(a, t)=0;

 

sys:=[pde[1],bc[1],pde[2],bc[2], u1(x=0,t)=u2(x=0,t), 

D[2](u1)(x,0)=D[2](u2)(x,0)

]

pdsolve(sys);

 

a and L is arbitrary constanta

anyone can help? The last boundary conditions I mean du1/dx=du2/dx at x=0

How can i solve this problem? 
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