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\begin{document}

\title{Boundary conditions at a thin membrane for normal diffusion, classical
subdiffusion, and slow subdiffusion processes}



\author[1]{Tadeusz Kosztolowicz}%
\author[2]{Aldona Dutkiewicz}%
\affil[1]{Jan Kochanowski University in Kielce}%
\affil[2]{Adam Mickiewicz University}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
We consider three different diffusion processes in a system with a thin
membrane: normal diffusion, classical subdiffusion, and slow
subdiffusion. We conduct the considerations following the rule:
\{\textbackslash{}it If a diffusion equation is derived from a certain
theoretical model, boundary conditions at a thin membrane should also be
derived from this model with additional assumptions taking into account
selective properties of the membrane\}. To derive diffusion equations
and boundary conditions at a thin membrane, we use a particle random
walk model in one-dimensional membrane system in which space and time
variables are discrete. Then we move from discrete to continuous
variables. We show that the boundary conditions depend on both selective
properties of the membrane and a type of diffusion in the system.%
\end{abstract}%



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