On a model of target detection in molecular communication networks

Hirotada Honda; Hirotada Honda

doi:10.3934/nhm.2019025

Networks and Heterogeneous Media

2019, Volume 14, Issue 4: 633-657. doi: 10.3934/nhm.2019025

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On a model of target detection in molecular communication networks

Hirotada Honda ^,

1-7-11, Akabanedai, Kita-Ku, Tokyo 115-0053, Japan

Received: 01 June 2018 Revised: 01 June 2019
Primary: 35K61, 35Q92; Secondary: 92C17

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.
- Molecular communication,
- target detection,
- global-in-time solvability
Citation: Hirotada Honda. On a model of target detection in molecular communication networks[J]. Networks and Heterogeneous Media, 2019, 14(4): 633-657. doi: 10.3934/nhm.2019025

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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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