Nonanalyticity of solutions to ${\partial }_{t}u=\partial {²}_{x}u+u²$

Grzegorz Łysik. "Nonanalyticity of solutions to $∂_{t}u = ∂²_{x}u + u²$." Colloquium Mathematicae 95.2 (2003): 255-266. <http://eudml.org/doc/284420>.

@article{GrzegorzŁysik2003,
abstract = {It is proved that the solution to the initial value problem $∂_\{t\}u = ∂²_\{x\}u + u²$, u(0,x) = 1/(1+x²), does not belong to the Gevrey class $G^s$ in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.},
author = {Grzegorz Łysik},
journal = {Colloquium Mathematicae},
keywords = {semilinear heat equation; Gevrey spaces; binomial estimates},
language = {eng},
number = {2},
pages = {255-266},
title = {Nonanalyticity of solutions to $∂_\{t\}u = ∂²_\{x\}u + u²$},
url = {http://eudml.org/doc/284420},
volume = {95},
year = {2003},
}

TY - JOUR
AU - Grzegorz Łysik
TI - Nonanalyticity of solutions to $∂_{t}u = ∂²_{x}u + u²$
JO - Colloquium Mathematicae
PY - 2003
VL - 95
IS - 2
SP - 255
EP - 266
AB - It is proved that the solution to the initial value problem $∂_{t}u = ∂²_{x}u + u²$, u(0,x) = 1/(1+x²), does not belong to the Gevrey class $G^s$ in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
LA - eng
KW - semilinear heat equation; Gevrey spaces; binomial estimates
UR - http://eudml.org/doc/284420
ER -