Temat: first 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:: 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

Skocz do pozycji: 3.

Tytuł:: Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Autorzy:: Rencławowicz, Joanna
Zajączkowski, Wojciech
Powiązania:: https://bibliotekanauki.pl/articles/1339037.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: relativistic hydrodynamics
symmetrization
existence
system of hyperbolic equations of the first order
initial-boundary value problem
Opis:: Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method of successive approximations.
Źródło:: Applicationes Mathematicae; 1998-1999, 25, 2; 221-252
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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