- Tytuł:
- Nonlinear Heat Equation with a Fractional Laplacian in a Disk
- Autorzy:
- Varlamov, Vladimir
- Powiązania:
- https://bibliotekanauki.pl/articles/965893.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
nonlinear heat equation
long-time asymptotics
fractional Laplacian
initial-boundary value problem in a disk - Opis:
- 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.
- Źródło:
-
Colloquium Mathematicum; 1999, 81, 1; 101-122
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł