On a model of target detection in molecular communication networks

Hirotada Honda

doi:10.3934/nhm.2019025

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

This issue Previous Article Next Article Well-balanced scheme for gas-flow in pipeline networks

On a model of target detection in molecular communication networks

Hirotada Honda^,

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

^* Corresponding author: Hirotada Honda
^* Corresponding author: Hirotada Honda

Received: May 31, 2018

Revised: May 31, 2019

Published: November 2019

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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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Mathematics Subject Classification: Primary: 35K61, 35Q92; Secondary: 92C17.

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