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On the Growth in Time of Sobolev Norms for TimeDependent Linear Generalized KdV-typeEquations |
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KeyWord:Sobolev norms Time dependent linear generalized KdV-type equa-
tion Fixed analytic potential |
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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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