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Your search keyword '"Lyu, Ming-Jiea"' showing total 16 results
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16 results on '"Lyu, Ming-Jiea"'

2. Space-time behavior of the solution to the Boltzmann equation with soft potentials

Author

Lin, Yu-Chu, Lyu, Ming-Jiea, Wang, Haitao, and Wu, Kung-Chien

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper, we get the quantitative space-time behavior of the full Boltzmann equation with soft potentials ($-2<\gamma <0$) in the close to equilibrium setting, under some velocity decay assumption, but without any Sobolev regularity assumption on the initial data. We find that both the large time and spatial behaviors depend on the velocity decay of the initial data and the exponent $\gamma$. The key step in our strategy is to obtain the $L^{\infty }$ bound of a suitable weighted full Boltzmann equation directly, rather than using Green's function and Duhamel's principle to construct the pointwise structure of the solution as in the paper: T.-P. Liu and S.-H. Yu, The Green function and large time behavier of solutions for the one-dimensional Boltzmann equation, Commun. Pure App. Math.,(2004). This provides a new thinking in the related study.

Published
2021

5. Force stability of the Boltzmann equations.

Author

Lyu, Ming-Jiea and Wu, Kung-Chien

Subjects
*EQUATIONS
Abstract

In this paper, we consider the Boltzmann equation with external force in the whole space, where the collision kernel is assumed to be hard potential and cutoff. We prove that the solutions of such Boltzmann equations are L p (1 ≤ p < ∞) stable under the perturbation of external force. Our estimate is based on the gradient estimate of the solution. The key step of this paper is to estimate the solutions of the equations propagate in different forward bi-characteristic. [ABSTRACT FROM AUTHOR]

Published
2024
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7. Covering relations for coupled map networks

Author

Bunimovich, Leonid, Li, Ming-Chia, and Lyu, Ming-Jiea

Subjects
Mathematics - Dynamical Systems, 37C15, 37C75, 37B10, 37B40, 37L60
Abstract

Following [6,12], we study coupled map networks over arbitrary finite graphs. An estimate from below for a topological entropy of a perturbed coupled map network via a topological entropy of an unperturbed network by making use of the covering relations for coupled map networks is obtained. The result is quite general, particularly no assumptions on hyperbolicity of a local dynamics or linearity of coupling are made.

Published
2011

15. Covering relations and Lyapunov condition for topological conjugacy.

Author

Li, Ming-Chia and Lyu, Ming-Jiea

Subjects
*LYAPUNOV functions, *TOPOLOGICAL spaces, *CONJUGACY classes, *DYNAMICAL systems, *INVARIANTS (Mathematics)
Abstract

In this paper, we study stability of non-autonomous discrete dynamical systems. For a two-sided non-autonomous systems with covering relations determined by a transition matrixA, we show that any smallC0perturbed system has a sequence of compact invariant sets restricted to which the system is topologically semi-conjugate to σA, the two-sided subshift of finite type induced byA. Together with Lyapunov condition of good rate, the semi-conjugacy will become conjugacy. Moreover, if the Lyapunov condition is strict and has perfect rate, then any smallC1perturbed systems is topological conjugate to σA. We also study topological chaos of one-sided systems and systems with limit functions. Lack of hyperbolicity and the time dependence of the rate prevent us from applying classical hyperbolic results or earlier works for autonomous systems: cone condition and Lyapunov function. Two examples are provided to demonstrate the existence of a non-trivial, non-hyperbolic invariant and essential of controlling rate. [ABSTRACT FROM AUTHOR]

Published
2016
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