# Nonlinear Heat Equation with a Fractional Laplacian in a Disk

Colloquium Mathematicae (1999)

- Volume: 81, Issue: 1, page 101-122
- ISSN: 0010-1354

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topVarlamov, Vladimir. "Nonlinear Heat Equation with a Fractional Laplacian in a Disk." Colloquium Mathematicae 81.1 (1999): 101-122. <http://eudml.org/doc/210722>.

@article{Varlamov1999,

abstract = {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.},

author = {Varlamov, Vladimir},

journal = {Colloquium Mathematicae},

keywords = {nonlinear heat equation; long-time asymptotics; fractional Laplacian; initial-boundary value problem in a disk; global-in-time mild solution; eigenfunction expansions; perturbation theory; long-time asymptotic behaviour},

language = {eng},

number = {1},

pages = {101-122},

title = {Nonlinear Heat Equation with a Fractional Laplacian in a Disk},

url = {http://eudml.org/doc/210722},

volume = {81},

year = {1999},

}

TY - JOUR

AU - Varlamov, Vladimir

TI - Nonlinear Heat Equation with a Fractional Laplacian in a Disk

JO - Colloquium Mathematicae

PY - 1999

VL - 81

IS - 1

SP - 101

EP - 122

AB - 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.

LA - eng

KW - nonlinear heat equation; long-time asymptotics; fractional Laplacian; initial-boundary value problem in a disk; global-in-time mild solution; eigenfunction expansions; perturbation theory; long-time asymptotic behaviour

UR - http://eudml.org/doc/210722

ER -

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