Regularity theorems for a biological network formulation model in two space dimensions

Xiangsheng Xu

doi:10.3934/krm.2018018

Article Contents

2018, Volume 11, Issue 2: 397-408. Doi: 10.3934/krm.2018018

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Regularity theorems for a biological network formulation model in two space dimensions

Xiangsheng Xu

Department of Mathematics & Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Received: November 30, 2016

Revised: April 30, 2017

Published: March 2018

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Abstract

We present several regularity results for a biological network formulation model originally introduced by D. Cai and D. Hu [13]. A consequence of these results is that a stationary weak solution must be a classical one in two space dimensions. Our mathematical analysis is based upon the weakly monotone function theory and Hardy space methods.

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Mathematics Subject Classification: Primary: 35D30, 35Q99; Secondary: 35A01.

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