Maillet type theorem and Gevrey regularity in time of solutions to nonlinear partial differential equations

• Autorzy: Hidetoshi Tahara
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35G20: Nonlinear higher-order equations
• 35B65: Smoothness and regularity of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2012
• Tom: 97
• Numer: 1
• Strony: 125-140

Daty

wydano

2012

Twórcy

autor

Hidetoshi Tahara

• Department of Information and Communication Sciences, Sophia University, Kioicho, Chiyoda-ku, Tokyo, 102-8554 Japan

Identyfikatory

DOI

10.4064/bc97-0-9