Taiwanese Journal of Mathematics

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

Yutian Lei

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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 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.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 425-446.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405799

Digital Object Identifier
doi:10.11650/twjm/1500405799

Mathematical Reviews number (MathSciNet)
MR2655779

Zentralblatt MATH identifier
1204.35031

Subjects
Primary: 35B25: Singular perturbations 35K65: Degenerate parabolic equations 35Q60: PDEs in connection with optics and electromagnetic theory

Keywords
$p$-Ginzburg-Landau equations location of zeros Holder convergence

Citation

Lei, Yutian. CONVERGENCE OF A RADIAL SOLUTION TO AN INITIAL-BOUNDARY VALUE PROBLEM OF $p$-GINZBURG-LANDAU TYPE. Taiwanese J. Math. 14 (2010), no. 2, 425--446. doi:10.11650/twjm/1500405799. https://projecteuclid.org/euclid.twjm/1500405799


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