Abstract
This paper is concerned with a target-detection model using bio-nanomachines in the human body that is actively being discussed in the field of molecular communication networks. Although the model was originally proposed as spatially one-dimensional, here we extend it to two dimensions and analyze it. After the mathematical formulation, we first verify the solvability of the stationary problem, and then the existence of a strong global-in-time solution of the non-stationary problem in Sobolev–Slobodetskiĭ space. We also show the non-negativeness of the non-stationary solution.
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