Nonlinear Heat Equation with a Fractional Laplacian in a Disk
Varlamov, Vladimir
Colloquium Mathematicae, Tome 79 (1999), p. 101-122 / Harvested from The Polish Digital Mathematics Library
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For the nonlinear heat equation with a fractional Laplacian ut+(-Δ)α/2u=u2, 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:210722 
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     year = {1999},
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Varlamov, Vladimir. Nonlinear Heat Equation with a Fractional Laplacian in a Disk. Colloquium Mathematicae, Tome 79 (1999) pp. 101-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i1p101bwm/

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