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 $(\dagger)$ denotes a real valued unknown function of the real variables and . denotes a fixed positive integer. It is assumed that is continuous in and Gevrey in . in (*) and in $(\dagger)$ are called shrinkings, since they satisfy the conditions sup and sup, respectively.
Citation
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
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