A vector field method on the distorted Fourier side and decay for wave equations with potentials. Memoirs of the American Mathematical Society; Bd. volume 241, number 1142 (3rd of 4 numbers).

Donninger, Roland; Krieger, Joachim

ISBN 10: 1470418738 / ISBN 13: 9781470418731

Published by Providence, American Mathematical Society, 2016

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03364 9781470418731 Sprache: Englisch Gewicht in Gramm: 150.

Seller Inventory # 2489271

Bibliographic Details

• Title: A vector field method on the distorted Fourier side and decay for wave equations with potentials. Memoirs of the American Mathematical Society; Bd. volume 241, number 1142 (3rd of 4 numbers).
• Publisher: Providence, American Mathematical Society
• Publication Date: 2016
• Language: English
• ISBN 10: 1470418738
• ISBN 13: 9781470418731
• Binding: Softcover
• Condition: Gut
• Weight: 150 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

The authors study the Cauchy problem for the one-dimensional wave equation ∂ 2 t u (t , x) − ∂ 2 x u (t , x) V (x)u (t , x) = 0. The potential V is assumed to be smooth with asymptotic behavior V (x) ∼ − 1 4 x−2 as x →∞. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t ∂t x∂x , where the latter are obtained by employing a vector field method on the “distorted” Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is funda­mental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, “Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space”, preprint (2013).

About the Author

Roland Donninger, and Joachim Krieger, Ecole Polytechnique Federale de Lausanne, Switzerland.