Nonanalyticity of solutions to ∂tu=∂²xu+u²
Grzegorz Łysik
Colloquium Mathematicae, Tome 96 (2003), p. 255-266 / Harvested from The Polish Digital Mathematics Library
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It is proved that the solution to the initial value problem ∂tu=∂²xu+u², u(0,x) = 1/(1+x²), does not belong to the Gevrey class Gs in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:284420 
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     author = {Grzegorz \L ysik},
     title = {Nonanalyticity of solutions to $$\partial$\_{t}u = $\partial$$^2$\_{x}u + u$^2$$
            },
     journal = {Colloquium Mathematicae},
     volume = {96},
     year = {2003},
     pages = {255-266},
     zbl = {1024.35022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-9}
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Grzegorz Łysik. Nonanalyticity of solutions to $∂_{t}u = ∂²_{x}u + u²$
            . Colloquium Mathematicae, Tome 96 (2003) pp. 255-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-9/