Classical solution of a PDE system stemming from auxin transport model for leaf venation

Li, Bin; Shen, Jieqiong

doi:10.1090/proc/14951

Classical solution of a PDE system stemming from auxin transport model for leaf venation
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by Bin Li and Jieqiong Shen PDF

Proc. Amer. Math. Soc. 148 (2020), 2565-2578 Request permission

Abstract:

This paper deals with the general regularity of solutions to a parabolic-elliptic system which is proposed by Haskovec, Jönsson, Kreusser, and Markowich to model the auxin transport for leaf venation. From very recent results it is known that for this parabolic-elliptic system associated with no-flux boundary conditions there exists a global weak solution. In this work, we present that whenever one enhances the regularity of the initial data, such weak solution can become more regular and thus the corresponding parabolic-elliptic system possesses a global classical solution. Moreover, the classical solution is uniformly bounded by seeking some suitable a priori estimates.

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