Location of Zeros for the Weak Solution to a $p$-Ginzburg-Landau Problem

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.