# sw NLPDE Z~i[

## sw NLPDE Z~i[

̃Z~i[͔`𒆐Sɉ͂̌Ɋւē_Z~i[łD
ւ̃ANZX

F_uYCCݖ{WC rcO

### ̃Z~i[̗\

2014 N 8 22 ijj Ԗ
sw w 3 251
u
Felipe Linares iInstituto Nacional de Matemática Pura e Aplicada, Brazilj
u
Propagation of regularity and decay of solutions to the $k$-generalized Korteweg-de Vries equation
uv|
We will discuss special regularity and decay properties of solutions to the IVP associated to the $k$-generalized KdV equations. In particular, for datum $u_0\in H^{3/4^+}(\R)$ whose restriction belongs to $H^k((b,\infty))$ for some $k\in \Z^+$ and $b\in \R$ we prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^k((\beta,\infty))$ for any $\beta \in \R$ and any $t\in (0,T)$. Thus, this type of regularity propagates with infinite speed to its left as time evolves.

### ̃Z~i[̗\

8 22
Felipe Linares iIMPA, Brazilj