Temat: generalized solutions - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Skocz do pozycji: 2.

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

Informacja