CONVERGENCE OF A RADIAL SOLUTION TO AN INITIAL-BOUNDARY VALUE PROBLEM OF $p$-GINZBURG-LANDAU TYPE

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 addition, the author also consider the Holder convergence of the solution when the parameter $\varepsilon$ tends to zero. The convergence is derived by establishing a uniform gradient estimate for the regularized solution of the system.