eqns={D[c1[t,x],t]==D[c1[t,x],x,x],D[c2[t,y],t]==D[c2[t,y],y‌​,y]};
bcs={c1[t,0]==1,c1[t,1]==c2[t,1],Derivative[0, 1][c1][t, 1] ==
    Derivative[0, 1][c2][t, 1],c2[t,2]==Exp[-1000*t]};
ics={c1[0,x]==1,c2[0,y]==1}; Tmax=0.5;
sol=NDSolveValue[{eqns,bcs,ics},{c1,c2},{t,0,Tmax},{x,0,1},{‌​y,1,2}]