Autor: Karch, Grzegorz - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Long-time asymptotics of solutions to some nonlinear wave equations
Autorzy:: Karch, Grzegorz
Powiązania:: https://bibliotekanauki.pl/articles/1207640.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: In this paper, we survey some recent results on the asymptotic behavior, as time tends to infinity, of solutions to the Cauchy problems for the generalized Korteweg-de Vries-Burgers equation and the generalized Benjamin-Bona-Mahony-Burgers equation. The main results give higher-order terms of the asymptotic expansion of solutions.
Źródło:: Banach Center Publications; 2000, 52, 1; 133-146
0137-6934
Pojawia się w:: Banach Center Publications
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
Autorzy:: Karch, Grzegorz
Powiązania:: https://bibliotekanauki.pl/articles/1294727.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: asymptotic behavior of solutions
dispersive equations
parabolic conservation laws
oscillatory integrals
Opis:: We study the decay in time of the spatial $L^p$-norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.
Źródło:: Annales Polonici Mathematici; 1997, 67, 1; 65-86
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
Autorzy:: Karch, Grzegorz
Powiązania:: https://bibliotekanauki.pl/articles/1205809.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: generalized wave equation with damping
the Cauchy problem
large time behavior of solutions
selfsimilar solutions
Opis:: Large time behavior of solutions to the generalized damped wave equation $u_{tt} +A u_t +ν B u+F(x,t,u,u_t,∇ u) = 0$ for $(x,t)∈ ℝ^n × [0,∞)$ is studied. First, we consider the linear nonhomogeneous equation, i.e. with F = F(x,t) independent of u. We impose conditions on the operators A and B, on F, as well as on the initial data which lead to the selfsimilar large time asymptotics of solutions. Next, this abstract result is applied to the equation where $Au_t = u_t$, $Bu = -Δu$, and the nonlinear term is either $|u_t|^{q-1}u_t$ or $|u|^{α-1}u$. In this case, the asymptotic profile of solutions is given by a multiple of the Gauss-Weierstrass kernel. Our method of proof does not require the smallness assumption on the initial conditions.
Źródło:: Studia Mathematica; 2000, 143, 2; 175-197
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: A Neumann problem for a convection-diffusion equation on the half-line
Autorzy:: Biler, Piotr
Karch, Grzegorz
Powiązania:: https://bibliotekanauki.pl/articles/1207965.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Neumann problem
asymptotics of solutions.
convection-diffusion equation
Opis:: We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.
Źródło:: Annales Polonici Mathematici; 2000, 74, 1; 79-95
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Asymptotics for multifractal conservation laws
Autorzy:: Biler, Piotr
Karch, Grzegorz
Woyczynski, Wojbor
Powiązania:: https://bibliotekanauki.pl/articles/1216945.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: generalized Burgers equation
fractal diffusion
asymptotics of solutions
Opis:: We study asymptotic behavior of solutions to multifractal Burgers-type equation $u_t + f(u)_x = Au$, where the operator A is a linear combination of fractional powers of the second derivative $-∂^2/ ∂ x^2$ and f is a polynomial nonlinearity. Such equations appear in continuum mechanics as models with fractal diffusion. The results include decay rates of the $L^p$-norms, 1 ≤ p ≤ ∞, of solutions as time tends to infinity, as well as determination of two successive terms of the asymptotic expansion of solutions.
Źródło:: Studia Mathematica; 1999, 135, 3; 231-252
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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