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

• Autorzy: Grzegorz Łysik
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35K05: Heat equation
• 35K15: Initial value problems for second-order parabolic equations
• 11B65: Binomial coefficients; factorials; q -identities
• 35A20: Analytic methods, singularities
• 35A10: Cauchy-Kovalevskaya theorems
• 05A10: Factorials, binomial coefficients, combinatorial functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 95
• Numer: 2
• Strony: 255-266

Daty

wydano

2003

Twórcy

autor

Grzegorz Łysik

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm95-2-9