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Necessary and sufficient condition for existence and uniqueness of the solution of Cauchy problem for holomorphic Fuchsian operators.

Terbeche, Mekki (2001)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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

Grzegorz Łysik (2003)

Colloquium Mathematicae

It is proved that the solution to the initial value problem $\partial_{t} u = \partial ²_{x} u + u ²$ , 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.

Currently displaying 1 – 2 of 2

Page 1

Displaying 1 – 2 of 2

Necessary and sufficient condition for existence and uniqueness of the solution of Cauchy problem for holomorphic Fuchsian operators.

Nonanalyticity of solutions to ∂ t u = ∂ ² x u + u ²

Currently displaying 1 – 2 of 2

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