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.