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• # Artykuł - szczegóły

## Banach Center Publications

2012 | 97 | 1 | 125-140

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

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.

125-140

wydano
2012

### Twórcy

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