Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We will consider the nonlinear partial differential equation <br> $t^{γ}(∂/∂t)^{m}u = F(t,x,{(∂/∂t)^{j}(∂/∂x)^{α}u}_{j+|α|≤L,j<m})$ (E) <br>(with γ ≥ 0 and 1 ≤ m ≤ L) and show the following two results: (1) (Maillet type theorem) if (E) has a formal solution it is in some formal Gevrey class, and (2) (Gevrey regularity in time) if (E) has a solution $u(t,x) ∈ C^{∞}([0,T],𝓔^{σ}(V))$ it is in some Gevrey class also with respect to the time variable t. It will be explained that the mechanism of these two results are quite similar, but still there appears some difference between them which is very interesting to the author.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
125-140
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- Department of Information and Communication Sciences, Sophia University, Kioicho, Chiyoda-ku, Tokyo, 102-8554 Japan
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-9