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Long-Time Asymptotics of Kinetic Models of Granular Flows

Archive for Rational Mechanics and Analysis, 2004
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LI H., TOSCANI, GIUSEPPE
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Sharp Long-Time Asymptotics for Chemotaxis with Free Boundary

SIAM Journal on Mathematical Analysis, 2021
The authors study the existence and behavior of the global solution to the free boundary value problem for the following nonlinear Patlak-Keller-Segel system: \[ \left\{ \begin{aligned} &\rho_t = \Delta \rho^m - \nabla \cdot (\rho \nabla c), \quad \mathbf{x} \in \Omega, ~ t \geq 0,\\ &-\Delta c = \rho, \end{aligned} \right.
Li, Hai-Liang, Perthame, Benoít, Wen, Xinmei   +2 more
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Long-Time Asymptotics Of  the Hunter-Saxton Equation on the Line

Journal of Differential Equations, 2023
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Luman Ju, Kai Xu, Engui Fan
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Long-time Asymptotic Behavior of Lax-Friedrichs Scheme

Journal of Partial Differential Equations, 1993
Der Verfasser untersucht die asymptotische Stabilität des Lax- Friedrichs Schema. Es wird bewiesen, daß die Lösung im ungeraden bzw. geraden Knoten nach zwei fortschreitenden Wellen strebt. Zunächst werden skalare Gleichungen betrachtet. Es wird bewiesen, daß die Lösung \(\ell^ 2\)-asymptotisch stabil ist, wenn der Anfangswert eine schwache Störung auf
Ying, Lungan, Zhou, Tie
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Long time asymptotics for the shrinking wiener sausage

Communications on Pure and Applied Mathematics, 1990
Let \((Z_ t\); \(t\geq 0)\) be the Brownian motion in \({\mathbb{R}}^ d\) (d\(\geq 2)\) and let \(W^{\rho (.),C}\) be the shrinking Wiener sausage given by \(W_ s^{\rho (s),C}=\cup_{0\leq u\leq s}Z_ u-\rho (s)C,\) where C is a nonpolar compact set in \({\mathbb{R}}^ d\) and \(\rho\) is a non-negative bounded function such that, for \(d\geq 3\), \(\rho (
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Rigorous Derivation of the Long-Time Asymptotics for Reversible Binding

Physical Review Letters, 2000
Using an iterative solution in Laplace-Fourier space, we supply a rigorous mathematical proof for the long-time asymptotics of reversible binding in one dimension. The asymptotic power law and its concentration dependent prefactor result from diffusional and many-body effects which, unlike for the corresponding irreversible reaction and in classical ...
, Gopich, , Agmon
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Long-time Asymptotic for the Damped Boussinesq Equation in a Circle

Journal of Partial Differential Equations, 2005
Summary: The first initial-boundary value problem for the following equation \[ u_{tt}- a\Delta u_{tt}- 2b\Delta u_t= \alpha\Delta^3 u- \beta\Delta^2 u+\Delta u+ \gamma\Delta(u^2) \] in a unit circle is considered. Existence of strong solution is established in the space \(C^0([0,\infty), H^s_r(0,1))\), \(s< 7/2\), and the solutions are constructed in ...
Zhang, Yi, Lin, Qun, Lai, Shaoyong
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Long Time Asymptotics for Quantum Particles in a Periodic Potential

Physical Review Letters, 1996
Summary: We study a quantum particle in a periodic potential and subject to slowly varying electromagnetic potentials. It is proved that, in the Heisenberg picture, the scaled position operator \(\epsilon \mathbf x(\epsilon^{-1}t)\) has a limit as \(\epsilon\to 0\).
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Long-time asymptotics of the mean-field magnetohydrodynamics equation

Journal of Physics A: Mathematical and General, 2001
Summary: It is shown that a magnetic field satisfying the mean-field magnetohydrodynamics equation with zero mean velocity and without energy input from the outside possesses a Lyapunov function, which is a combination of magnetic energy and helicity. As a consequence, if the mean magnetic field remains uniformly bounded for all time, the field tends ...
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LONG TIME ASYMPTOTICS OF DIFFUSION IN A RANDOM MEDIUM

Modern Physics Letters B, 1995
Based upon the assumption that the trajectory of a particle subjected to a thermal noise and to a divergenceless random force has the Gaussian distribution, the long time asymptotics of the particle displacement are analyzed. The results are in agreement with that of the renormalization group analysis.
XIAO-HONG WANG, KE-LIN WANG
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