Geodesic
Nonanalyticity of solutions to ∂tu=∂x2u+u2
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 ∂tu=∂x2u+u2, u(0,x)=1/(1+x2), does not belong to the Gevrey class Gs in time for 0≤s1. The proof is based on an estimation of a double sum of products of binomial coefficients.
DOI : 10.4064/cm95-2-9
Mots-clés : 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},
     publisher = {mathdoc},
     volume = {95},
     number = {2},
     year = {2003},
     doi = {10.4064/cm95-2-9},
     language = {en},
     url = {https://geodesic-test.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
PB  - mathdoc
UR  - https://geodesic-test.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
%I mathdoc
%U https://geodesic-test.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. https://geodesic-test.mathdoc.fr/articles/10.4064/cm95-2-9/
  • Holmes, John Well-posedness and regularity of the generalized Burgers equation in periodic Gevrey spaces, Journal of Mathematical Analysis and Applications, Volume 454 (2017) no. 1, pp. 18-40 | DOI:10.1016/j.jmaa.2017.04.045 | Zbl:1367.35054
  • Łysik, Grzegorz; Michalik, Sławomir Formal solutions of semilinear heat equations, Journal of Mathematical Analysis and Applications, Volume 341 (2008) no. 1, pp. 372-385 | DOI:10.1016/j.jmaa.2007.10.005 | Zbl:1139.35035
  • Łysik, G. Non-analyticity in time of solutions to the KdV equation, Zeitschrift für Analysis und ihre Anwendungen, Volume 23 (2004) no. 1, pp. 67-93 | DOI:10.4171/zaa/1188 | Zbl:1059.35120

Cité par 3 documents. Sources : zbMATH