Geodesic
Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$
Grzegorz Łysik 1
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_cm95_2_9,
     author = {Grzegorz {\L}ysik},
     title = {Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$},
     journal = {Colloquium Mathematicum},
     pages = {255--266},
     year = {2003},
     volume = {95},
     number = {2},
     doi = {10.4064/cm95-2-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-9/}
}
TY  - JOUR
AU  - Grzegorz Łysik
TI  - Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$
JO  - Colloquium Mathematicum
PY  - 2003
SP  - 255
EP  - 266
VL  - 95
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-9/
DO  - 10.4064/cm95-2-9
LA  - en
ID  - 10_4064_cm95_2_9
ER  - 
%0 Journal Article
%A Grzegorz Łysik
%T Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$
%J Colloquium Mathematicum
%D 2003
%P 255-266
%V 95
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-9/
%R 10.4064/cm95-2-9
%G en
%F 10_4064_cm95_2_9
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

Cité par Sources :