Boundary null-controllability of 1-D coupled parabolic systems with Kirchhoff-type conditions

The main concern of this article is to investigate the boundary controllability some $$2\times 2$$ one-dimensional parabolic systems with both interior and couplings: coupling chosen be linear constant coefficient while one considered by means Kirchhoff-type condition at end domain. We consider here Dirichlet control acting only on two state components other In particular, we show that properties change depending which component system being applied. Regarding this, point out choices Kirchhoff parameter play a crucial role deduce positive or negative results. Further pursue numerical study based well-known penalized HUM approach. make discretization for general interior-boundary coupled system, mainly incorporate effects couplings into discrete setting. This allows us illustrate our theoretical results as well experiment more examples fit under framework, instance similar Neumann either components.