Temat: initial boundary value problem - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On the Kuramoto-Sivashinsky equation in a disk
Autorzy:: Varlamov, Vladimir
Powiązania:: https://bibliotekanauki.pl/articles/1208011.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: first initial-boundary value problem
long-time asymptotics
Kuramoto-Sivashinsky equation
disk
Opis:: We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed solution and its asymptotics with respect to the nonlinearity constant. The method can work for other dissipative parabolic equations with dispersion.
Źródło:: Annales Polonici Mathematici; 2000, 73, 3; 227-256
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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

Skocz do pozycji: 3.

Tytuł:: Long-time asymptotics for the nonlinear heat equation with a fractional Laplacian in a ball
Autorzy:: Varlamov, Vladimir
Powiązania:: https://bibliotekanauki.pl/articles/1206006.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: first initial-boundary value problem
nonlinear heat equation
construction of solutions
higher-order long-time asymptotics
fractional Laplacian
Opis:: The nonlinear heat equation with a fractional Laplacian $[u_t+(-Δ)^{α/2} u = u^2, 0 < α ≤ 2]$, is considered in a unit ball $B$. Homogeneous boundary conditions and small initial conditions are examined. For 3/2 + ε₁ ≤ α ≤ 2, where ε₁ > 0 is small, the global-in-time mild solution from the space $C⁰([0,∞), H₀^{κ}(B))$ with κ < α - 1/2 is constructed in the form of an eigenfunction expansion series. The uniqueness is proved for 0 < κ < α - 1/2, and the higher-order long-time asymptotics is calculated.
Źródło:: Studia Mathematica; 2000, 142, 1; 71-99
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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