How do I handle boundary conditions present in the region . Mathematica complains about the condition v [1 , t ] == u [1,t]. The condition should be given to this point!
NDSolve[{
D[u[x, t], t] + D[u[x, t], x] == -u[x, t],
D[v[x, t], t] + D[v[x, t], x] == -v[x, t],
u[x, 0] == E^-x,
v[x, 0] == E^(1 - x),
u[0, t] == 1,
v[1, t] == u[1, t]
},
{u[x, t], v[x, t]},
{x, 0, 2},
{t, 0, 5}]
Many thanks for any help ...
