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July, 2002 On the Cauchy problem for non linear PDEs in the Gevrey class with shrinkings
Masaki KAWAGISHI, Takesi YAMANAKA
J. Math. Soc. Japan 54(3): 649-677 (July, 2002). DOI: 10.2969/jmsj/1191593913

Abstract

In the article, the Cauchy problem of the form

(*) $\partial_{2}u(x,t)=f(u(x,t),\partial_{1}^{p}u(x,\alpha(t)t),x,t),\ u(x,0)=0$

or of the form

$(\dagger)$ $\partial_{2}u(x,t)=f(u(x,t), \partial_{1}^{p}u(\alpha(x,t)x,t),x,t),\ u(x,0)=0$

is studied. In (*) and $(\dagger)$ u(x,t) denotes a real valued unknown function of the real variables x and t. p denotes a fixed positive integer. It is assumed that f(u,v,x,t) is continuous in (u,v,x,t) and Gevrey in (u,v,x). α(t) in (*) and α(x,t) in $(\dagger)$ are called shrinkings, since they satisfy the conditions sup|α(t)|<1 and sup|α(x,t)|<1, respectively.

Citation

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Masaki KAWAGISHI. Takesi YAMANAKA. "On the Cauchy problem for non linear PDEs in the Gevrey class with shrinkings." J. Math. Soc. Japan 54 (3) 649 - 677, July, 2002. https://doi.org/10.2969/jmsj/1191593913

Information

Published: July, 2002
First available in Project Euclid: 5 October 2007

zbMATH: 1032.35059
MathSciNet: MR1900961
Digital Object Identifier: 10.2969/jmsj/1191593913

Subjects:
Primary: 35A10
Secondary: 35G25, 35R10

Rights: Copyright © 2002 Mathematical Society of Japan

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Vol.54 • No. 3 • July, 2002
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