Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
نویسندگان
چکیده
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. 2005 Elsevier SAS. All rights reserved. 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. 2005 Elsevier SAS. All rights reserved.
منابع مشابه
Global solutions of the derivative Schrödinger equation in a class of functions analytic in a strip
Lower bounds on the rate of decrease in time of a uniform radius of spatial analyticity for solutions of the derivative Schrödinger equation are derived. The bounds depend algebraically on time. They are valid as long as the initial datum is of order one in L2-norm and satisfies suitable spatial decay requirements on the real axis. © 2006 Elsevier Inc. All rights reserved.
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