Effect of a Membrane on Diffusion-Driven Turing Instability

Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to case two domains separated by a permeable membrane. To this aim, we study reaction–diffusion system with zero-flux boundary conditions external Kedem-Katchalsky inner use same approach as in classical analysis but applied operators. The introduction diagonalization for compact self-adjoint operators is needed. Here, instability proven addition new constraints, due presence permeability coefficients. perform explicit one-dimensional eigenvalue problem, combined simulations, validate theoretical results. Finally, observe formation discontinuous patterns which combines diffusion dissipative conditions, varying both