Blow-up time of strong solutions to a biological network formation model in high space dimensions

Xiangsheng Xu

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arXiv · 2109.03567

Blow-up time of strong solutions to a biological network formation model in high space dimensions

Xiangsheng Xu

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Abstract

We investigate the possible blow-up of strong solutions to a biological network formation model originally introduced by D. Cai and D. Hu \cite{HC}. The model is represented by an initial boundary value problem for an elliptic-parabolic system with cubic non linearity. We obtain an algebraic equation for the possible blow-up time of strong solutions. The equation yields information on how various given data may contribute to the blow-up of solutions. As a by-product of our development, we establish a $W^{1,q}$ estimate for solutions to an elliptic equation which shows the explicit dependence of the upper bound on the elliptic coefficients.

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Xiangsheng Xu. 2021-09-08. Blow-up time of strong solutions to a biological network formation model in high space dimensions. https://arxiv.org/abs/2109.03567

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