JournalsaihpcVol. 22, No. 6pp. 783–797

Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation

  • Zoran Grujić

    Department of Mathematics, University of Virginia, USA

  • Henrik Kalisch

    Centre for Mathematical Sciences, Lund University, Sweden

  • Jerry L. Bona

    Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, USA
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Abstract

The generalized Korteweg–de Vries equation has the property that solutions with initial data that are analytic in a strip in the complex plane continue to be analytic in a strip as time progresses. Established here are algebraic lower bounds on the possible rate of decrease in time of the uniform radius of spatial analyticity for these equations. Previously known results featured exponentially decreasing bounds.

Résumé

Si la donnée initiale est analytique sur une bande dans le plan complexe, alors la solution de l'équation de Korteweg et de Vries généralisée le reste pour tout temps. Nous montrons que la largeur de cette bande décroit algébriquement en temps. Les résultats antérieurs ne donnaient qu'un taux de décroissance exponentiel.

Cite this article

Zoran Grujić, Henrik Kalisch, Jerry L. Bona, Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 6, pp. 783–797

DOI 10.1016/J.ANIHPC.2004.12.004