ON THE PROPAGATION OF REGULARITY AND DECAY OF SOLUTIONS TO THE k-GENERALIZED KORTEWEG-DE VRIES EQUATION
نویسندگان
چکیده
We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u0 ∈H3/4 + (R) whose restriction belongs to H l((b,∞)) for some l ∈ Z+ and b ∈ R we prove that the restriction of the corresponding solution u(·, t) belongs to H l((β ,∞)) for any β ∈ R and any t ∈ (0,T ). Thus, this type of regularity propagates with infinite speed to its left as time evolves.
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