MR2239909
Mizuhara, Ryuichiro
Ryuichiro MIZUHARA
The Initial Value Problem for Third and Fourth Order Dispersive Equations in One Space Dimension
Funkcialaj Ekvacioj. Serio Internacia
49
2006
1--38
http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-1/49_1.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2239909
We present the sufficient conditions for the $L^2$-well-posedness of the initial value problem for third and fourth order dispersive equations in one space dimension. In third order case and particular fourth order case, these conditions are also necessary. Tarama's pseudodifferential operators play crucial role in our proof.
Dispersive equations, Initial value problem, Well-posedness, Pseudodifferential calculus, Smoothing effect.
35G10, 35A07.
49-1
2006
The Initial Value Problem for Third and Fourth Order Dispersive Equations in One Space Dimension
MIZUHARA, Ryuichiro
Ryuichiro MIZUHARA
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