Volume 34, Issue 4
Location of Zeros for the Weak Solution to a p-Ginzburg-Landau Problem
10.13447/j.1674-5647.2018.04.09

Commun. Math. Res. , 34 (2018), pp. 363-370.

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• Abstract

This paper is concerned with the asymptotic behavior of the solution $u_\varepsilon$ of a $p$-Ginzburg-Landau system with the radial initial-boundary data. The author proves that the zeros of $u_\varepsilon$ in the parabolic domain $B_1(0)\times (0,\,T]$ locate near the axial line $\{0\}\times(0,\,T]$. In particular, all the zeros converge to this axial line when the parameter $\varepsilon$ goes to zero.