Geodesic
Nonlinear Heat Equation with a Fractional Laplacian in a Disk
Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 101-122.

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For the nonlinear heat equation with a fractional Laplacian $u_t + (-Δ)^{α/2} u = u^2$, 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.
DOI : 10.4064/cm-81-1-101-122
Keywords: nonlinear heat equation, long-time asymptotics, fractional Laplacian, initial-boundary value problem in a disk

Vladimir Varlamov 1

1 
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Vladimir Varlamov. Nonlinear Heat Equation with a Fractional Laplacian in a Disk. Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 101-122. doi : 10.4064/cm-81-1-101-122. http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-101-122/

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