Chinese Annals of Mathematics, Series B

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The rain on underground porous media Part I: Analysis of a richards model
Chinese Annals of Mathematics, Series B - Tập 34 - Trang 193-212 - 2013
Christine Bernardi, Adel Blouza, Linda El Alaoui
The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite eleme...... hiện toàn bộ
Stochastic fractional Anderson models with fractional noises
Chinese Annals of Mathematics, Series B - Tập 31 - Trang 101-118 - 2009
Yiming Jiang, Kehua Shi, Yongjin Wang
The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its Hölder continuity is studied. On the other hand, the absolute continuity of t...... hiện toàn bộ
Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables
Chinese Annals of Mathematics, Series B - Tập 33 - Trang 557-568 - 2012
Kam Chuen Yuen, Chuancun Yin
Let X 1,X 2, ... be a sequence of dependent and heavy-tailed random variables with distributions F 1, F 2, ... on (−∞,∞), and let τ be a nonnegative integer-valued random variable independent of the sequence {X k , k ≥ 1}. In this framework, the asymptotic behavior of the tail probabi...... hiện toàn bộ
Homoclinic flip bifurcations accompanied by transcritical bifurcation
Chinese Annals of Mathematics, Series B - Tập 32 - Trang 905-916 - 2011
Xingbo Liu
The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.
Global geometry of 3-body motions with vanishing angular momentum I
Chinese Annals of Mathematics, Series B - Tập 29 - Trang 1-54 - 2007
Wu-Yi Hsiang, Eldar Straume
Following Jacobi’s geometrization of Lagrange’s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor (U + h), where U and h are the potential function and the total energy, respectively. In the special case of 3-body motio...... hiện toàn bộ
Almost sure asymptotics for extremes of non-stationary Gaussian random fields
Chinese Annals of Mathematics, Series B - Tập 35 - Trang 125-138 - 2014
Zhongquan Tan, Yuebao Wang
In this paper, the authors prove an almost sure limit theorem for the maxima of non-stationary Gaussian random fields under some mild conditions related to the covariance functions of the Gaussian fields. As the by-products, the authors also obtain several weak convergence results which extended the existing results.
Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems
Chinese Annals of Mathematics, Series B - Tập 43 - Trang 1049-1070 - 2022
Yunmei Chen, Hongcheng Liu, Weina Wang
In this paper, the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems, where the nonconvex term is possibly nonsmooth. Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical perfor...... hiện toàn bộ
Transversal instability for the thermodiffusive reaction-diffusion system
Chinese Annals of Mathematics, Series B - Tập 36 - Trang 871-882 - 2015
Michal Kowalczyk, Benoît Perthame, Nicolas Vauchelet
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, and growth of bacterial colonies. Since a scalar equation generates usually stable waves, the simplest mathematical description relies on two-by-two reaction-diffusion systems. The authors’ interest is the extension of the Fisher/KPP...... hiện toàn bộ
Nonexistence of proper holomorphic maps between certain classical bounded symmetric domains
Chinese Annals of Mathematics, Series B - Tập 29 - Trang 135-146 - 2008
Ngaiming Mok
The author, motivated by his results on Hermitian metric rigidity, conjectured in [4] that a proper holomorphic mapping ƒ: Ω → Ω′ from an irreducible bounded symmetric domain Ω of rank ≥ 2 into a bounded symmetric domain Ω′ is necessarily totally geodesic provided that r′:= rank(Ω′) ≤ rank(Ω):= r. The Conjecture was resolved in the affirmative by I.-H. Tsai [8]. When the hypothesis r′ ≤ r is remov...... hiện toàn bộ
On a strongly damped wave equation for the flame front
Chinese Annals of Mathematics, Series B - Tập 31 - Trang 819-840 - 2010
Claude-Michel Brauner, Luca Lorenzi, Gregory I. Sivashinsky, Chuanju Xu
In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation (K-S). However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the ass...... hiện toàn bộ
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