Asymptotic stability of viscous contact wave to a radiation hydrodynamic limit model

This paper is concerned with the large time behavior of the solutions for 1D radiation hydrodynamic limit model without viscosity and its asymptotic stability of the viscous contact discontinuity wave under the smallness assumption of the strength of the contact wave and initial perturbations. The present pressure includes a fourth-order term about the absolute temperature from radiation effect which brings the main difficulty. Furthermore, the dissipative of the system is weaker for the lack of viscosity. All these make the problem more challenging. The prove is mainly based on the energy method, including normal and radial directions energy estimates.     

Asymptotic limit for condensate solutions in the Abelian Chern-Simons Higgs model

In this paper we show that the maximal solutions in the Abelian Chern-Simons Higgs model on a 't Hooft type periodic domain converges to and is a harmonic map. We also study asymptotic behaviors of the energy density.

     

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.     

Asymptotic limit for condensate solutions in the Abelian Chern-Simons Higgs model II

In this paper we show that the maximal condensate solutions in the Abelian Chern-Simons Higgs model converge to in higher norms, where is a harmonic map.

     

Stability of limit cycles in a pluripotent stem cell dynamics model

This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We then investigate the stability of the limit cycles yielded by the bifurcation using the normal form theory and the center manifold theorem. We illustrate our results with some numerics.     

Asymptotic expansions in functional limit theorems

Asymptotic expansions for a class of functional limit theorems are investigated. It is shown that the expansions in this class fit into a common scheme, defined by a sequence of functions h_n (ε₁,…, ε_n), n ≥ 1, of “weights” (for n observations), which are smooth, symmetric, compatible and have vanishing first derivatives at zero. Then $\text{h}{}_{\mathrm{n}}\text{(n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{,…, n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ admits an asymptotic expansion in powers of $\text{n}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$. Applications to quadratic von Mises functionals, the C.L.T. in Banach spaces, and the invariance principle are discussed.     

Asymptotic analysis of a singularly perturbed linear system with a singular limit pencil of matrices

With the help of perturbation methods and Newton diagrams, an asymptotic analysis is conducted of the general solution of a linear singularly perturbed system of ordinary differential equations in the case of degeneracy of a matrix multiplying the derivative in the approach of a small parameter to zero. It is assumed that the pencil of limit matrices of the system is singular and possesses a minimal index for rows and columns.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 106–122, January, 1992.     

Asymptotic stability of forced oscillations emanating from a limit cycle

Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the sign of the derivative of the associated bifurcation function at a zero. In this paper we show that, for analytic systems, this result is of topological nature. This means that it is enough to impose a change of sign at the zero, without any assumption on the succesive derivatives.     

Asymptotic limit of the Gross-Pitaevskii equation with general initial data

This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.     

Asymptotic arc-components of unimodal inverse limit spaces

We consider the inverse limit space (I,f) of a unimodal bonding map f as fixed bonding map. If f has a periodic turning point, then (I,f) has a finite non-empty set of asymptotic arc-components. We show how asymptotic arc-components can be determined from the kneading sequence of f. This gives an alternative to the substitution tiling space approach taken by Barge and Diamond [Ergodic Theory Dynamical Systems 21 (2001) 1333].     

Asymptotic expansions in the conditional central limit theorem

Let X_n, n , be i.i.d. with mean 0, variance 1, and E(¦X_n¦^r) < ∞ for some r 3. Assume that Cramér's condition is fulfilled. We prove that the conditional probabilities P(1/√n Σ_{i = 1}ⁿ X_i t¦B) can be approximated by a modified Edgeworth expansion up to order o(1/n^{(r − 2)/2)}), if the distances of the set B from the σ-fields σ(X₁, …, X_n) are of order O(1/n^{(r − 2)/2)}(lg n)^β), where β < −(r − 2)/2 for r and β < −r/2 for r . An example shows that if we replace β < −(r − 2)/2 by β = −(r − 2)/2 for r (β < −r/2 by β = −r/2 for r ) we can only obtain the approximation order O(1/n^{(r − 2)/2)}) for r (O(lg lgn/n^{(r − 2)/2)}) for r ).     

Asymptotic model of fields in a thin-walled structure with crack-like defects

The transition from two-dimensional (2D) wave propagation throughthe square periodic structure in anti-plane shear time-harmoniccase to a discretised model of a 2D lattice with masses connectedby springs is considered. A model of a defect in the middlepart of the thin-walled bridges is presented. As a first partof the asymptotic model, the effective transmission conditionin the vicinity of the transverse cut of the thin-walled bridgesis discussed. Then, a boundary layer determining the asymptoticexpansion of the field near the tip of the crack is constructed.Stress intensity factors are evaluated for deep cracks in thejunction regions. The corresponding boundary layer analysisis non-trivial and has not been attempted elsewhere.     

Asymptotic properties of excited states in the Thomas-Fermi limit

Excited states are stationary localized solutions of the Gross-Pitaevskii equation with a harmonic potential and a repulsive nonlinear term that have zeros on a real axis. The existence and the asymptotic properties of excited states are considered in the semi-classical (Thomas-Fermi) limit. Using the method of Lyapunov-Schmidt reductions and the known properties of the ground state in the Thomas-Fermi limit, we show that the excited states can be approximated by a product of dark solitons (localized waves of the defocusing nonlinear Schrödinger equation with nonzero boundary conditions) and the ground state. The dark solitons are centered at the equilibrium points where a balance between the actions of the harmonic potential and the tail-to-tail interaction potential is achieved.     

Asymptotic expansions in the central limit theorem for a branching Wiener process

Science China Mathematics - We consider a branching Wiener process in ?d, in which particles reproduce as a super-critical Galton-Watson process and disperse according to a Wiener process....     

Asymptotic analysis of a multiferroic model

Theoretical and Mathematical Physics - We consider a system of nonlinear autonomous differential equations that describe the orientation of the antiferromagnetic vector in a multiferroic film and...