On the Growth in Time of Sobolev Norms for Time Dependent Linear Generalized KdV-Type Equations

On the Growth in Time of Sobolev Norms for Time Dependent Linear Generalized KdV-Type Equations

Year:    2020

Author:    Chengming Cao, Xiaoping Yuan

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 3 : pp. 355–373

Abstract

We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobolev norms is polynomial in time for fixed analytic potential with admissible growth. If the initial data are given in a fixed smaller function space with more strict admissible growth conditions for $V (x,t)$, then the growth of previous Sobolev norms is at most logarithmic in time.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2020.355

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 3 : pp. 355–373

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Sobolev norms Time dependent linear generalized KdV-type equation Fixed analytic potential.

Author Details

Chengming Cao

Xiaoping Yuan