# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Nonanalyticity of solutions to $\partial _{t}u=\partial _{x}^2u+u^2$

### Tom 95 / 2003

Colloquium Mathematicum 95 (2003), 255-266 MSC: Primary 35A10, 35A20, 35K05, 35K15; Secondary 05A10, 11B65. DOI: 10.4064/cm95-2-9

#### Streszczenie

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 $0\le s<1$. The proof is based on an estimation of a double sum of products of binomial coefficients.

#### Autorzy

• Grzegorz ŁysikInstitute of Mathematics