Geodesic
Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$
Grzegorz Łysik1
1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland
Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 255-266.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is proved that the solution to the initial value problem $\partial _tu=\partial _x^2u+u^2$, $u(0,x)=1/(1+x^2)$, does not belong to the Gevrey class $G^s$ in time for $0\le s1$. The proof is based on an estimation of a double sum of products of binomial coefficients.
DOI : 10.4064/cm95-2-9
Keywords: proved solution initial value problem partial partial does belong gevrey class time proof based estimation double sum products binomial coefficients

Grzegorz Łysik 1

1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland 
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Grzegorz Łysik. Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$. Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 255-266. doi : 10.4064/cm95-2-9. http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-9/

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