Abstract: We give a new derivation of Robin boundary conditions and interface jump conditions for the diffusion equation in one dimension. To derive a Robin boundary condition, we consider the diffusion equation with a boundary condition that randomly switches between a Dirichlet and a Neumann condition. We prove that, in the limit of infinitely fast switching rate with the proportion of time spent in the Dirichlet state, denoted by $\rho$, approaching zero, the mean of the solution satisfies a Robin condition, with conductivity parameter determined by t...
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Mathematical analysis