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## Colloquium Mathematicum

1999 | 81 | 1 | 101-122
Tytuł artykułu

### Nonlinear Heat Equation with a Fractional Laplacian in a Disk

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
101-122
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-06
poprawiono
1999-02-01
Twórcy
autor
• Departamento de Matemáticas, Escuela Colombiana de Ingeniería, A.A. 14520, Bogotá, Colombia
Bibliografia
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• [21] V. V. Varlamov, Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation, Abstract Appl. Anal., 2 (1998), 97-115.
• [22] V. V. Varlamov, On the damped Boussinesq equation in a circle, Nonlinear Anal., to appear.
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Typ dokumentu
Bibliografia
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