Solve PDE with Multiple Boundary Conditions

Hi,

I want to solve PDE with Multiple Boundary Conditions.

But in terms of the problem I am interested in, there are two PDE in a different region.

For example, one set in the interval [0,1], and the other set in the interval [1,5]. The connection between the two regions is that the solutions must be continuous at x=1. The solution must also satisfy the boundary conditions like below

:https://www.mathworks.com/help/matlab/math/solve-bvp-with-multiple-boundary-conditions.html

I am wondering whether the problem also can be solved in PDE with a time derivative.

Thanks,

Dong Woo

[Torsten]

If you want to solve a stationary problem, take a look here:

https://uk.mathworks.com/help/matlab/math/solve-bvp-with-multiple-boundary-conditions.html

And here is an answer for time-dependent problems:

https://uk.mathworks.com/matlabcentral/answers/2049012-run-pdepe-solver-in-adjacent-domains-introduce-flux-bc-at-the-interface?s_tid=srchtitle

If this does not answer your question, please supply your equations, the computational domain, the interface and boundary conditions and initial conditions.