Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.     

A note on the eigenvalue ratio of vibrating strings

For vibrating strings with symmetric single-well densities, it is known that the ratio λ₂/λ₁1 is maximized when the density is constant. In this note, we extend this result to a class of symmetric densities.      

Analysis of Maxwell–Stefan systems for heat conducting fluid mixtures

The global-in-time existence of bounded weak solutions to the Maxwell–Stefan–Fourier equations in Fick–Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and the energy balance equation for the total energy. The diffusion and heat fluxes depend linearly on the gradients of the thermo-chemical potentials and the gradient of the temperature and include the Soret and Dufour effects. The cross-diffusion system exhibits an entropy structure, which originates from the thermodynamic modeling. The lack of positive definiteness of the diffusion matrix is compensated by the fact that the total mass density is constant in time. The entropy estimate yields the a.e. positivity of the partial mass densities and temperature. Also diffusion matrices are considered that degenerate for vanishing partial mass densities.     

On the eigenvalue ratio for vibrating strings

For vibrating strings with concave densities or symmetric single-barrier densities, the ratio of the first two eigenvalues is minimized when the density is constant; while, for vibrating strings with symmetric single-well densities, the ratio is maximized when the density is constant.

     

Nilpotent and recursive flows

In this paper we introduce a class of nonlinear vector fields on infinite dimensional manifolds such that the corresponding evolution equations can be solved with the same method one uses to solve ordinary differential equations with constant coeficients. Mostly, these equations are nonlinear partial differential equations. It is shown that these flows are characterized by a generalization of the ‘method of variation of constants’ which is widely used for second order problems to find general solutions out of particular ones. Invariant densities are constructed for these flows in a natural way. These invariant densities are providing an essential tool for solving initial value and boundary value problems for the equations under consideration. Many applications are presented     

A Lagrangian Approach for the Incompressible Navier‐Stokes Equations with Variable Density

We investigate the Cauchy problem for the inhomogeneous Navier‐Stokes equations in the whole n‐dimensional space. Under some smallness assumption on the data, we show the existence of global‐in‐time unique solutions in a critical functional framework. The initial density is required to belong to the multiplier space of \input amssym $\dot {B}^{n/p‐1}_{p,1}({\Bbb R}^n)$ . In particular, piecewise‐constant initial densities are admissible data provided the jump at the interface is small enough and generate global unique solutions with piecewise constant densities. Using Lagrangian coordinates is the key to our results, as it enables us to solve the system by means of the basic contraction mapping theorem. As a consequence, conditions for uniqueness are the same as for existence. © 2012 Wiley Periodicals, Inc.     

On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations

We discuss a nonlinear model of the spatial–time interaction among populations which reproduction and intensity of interaction depend on their spatial density. For the particular case of two populations with constant growth rates and competition coefficients we obtain analytical nonlinear waves of kink kind. The kinks are connected to propagation of the deviations from the stationary densities corresponding to fixed points in the phase space of the population densities. The kinks are coupled, i.e. the changes of the densities of the two populations are synchronous. Coupled kink solutions are obtained also for the general case of variable growth rates and variable coefficients of interactions.     

On Nonlinear Rayleigh-Taylor Instabilities

Some of the mathematical properties of the interface between two incompressible inviscid and immiscible fluids with different densities under the influence of a constant gravity field 9 are investigated. The purpose of this paper is to prove that linearly unstable modes for Rayleigh-Taylor instabilities give birth to nonlinear instabilities for the full nonlinear system. The main ingredient is a general instability theorem in an analytic framework which enables us to go from linear to nonlinear instabilities.     

Simultaneous Packing and Covering in the Euclidean Plane

 In this article we study the simultaneous packing and covering constants of two-dimensional centrally symmetric convex domains. Besides an identity result between translative case and lattice case and a general upper bound, exact values for some special domains are determined. Similar to Mahler and Reinhardt’s result about packing densities, we show that the simultaneous packing and covering constant of an octagon is larger than that of a circle.     

Lagrange中心型守恒格式

提出了Lagrange中心型守恒气体动力学格式．引入了当前时刻子网格密度与当前时刻网格声速产生的网格分片常数压力．初始网格密度乘以初始子网格体积得到子网格质量,这些子网格质量除以当前时刻子网格体积得到当前时刻子网格密度．应用网格分片常数压力,构造了满足动量守恒、总能量守恒的Lagrange中心型守恒气体动力学格式,格点速度以与网格面的数值通量相容的方式计算．对Saltzman活塞问题等进行了数值模拟,数值结果显示Lagrange中心型守恒气体动力学格式的有效性和精确性．     

Asymptotically minimax tests for nonparametric hypotheses concerning the distribution density

Asymptotically minimax goodness-of-fit, as well as symmetry, homogeneity, and independence tests are constructed, when it is known that the norm of the difference of the densities of the hypothesis and the alternative are bounded away from zero by a constant _n and the densities satisfy some smoothness conditions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 44–53, 1988.     

On well-posedness of incompressible two-phase flows with phase transitions: the case of non-equal densities

The basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics is studied. The latter means that the total energy is conserved and the total entropy is nondecreasing. We consider the case of constant but non-equal densities of the phases, complementing our previous paper (Prüss et?al. in Evol Equ Control Theory 1:171–194, 2012) where the case of equal densities is analyzed. The local well-posedness of such problems is proved by means of the technique of maximal L _p -regularity, in a configuration where the interface is nearly flat and initial data are small.     

一类非二次微分食饵—捕食系统的脉冲控制

利用脉冲微分方程的比较原理对一个具有功能反应函数为x~(1/2)的食饵—捕食生物模型进行研究.考虑到模型存在的不确定性,研究了捕食者的捕食率不但受食饵的密度大小影响,同时还受捕食者本身的密度影响的生物系统.通过脉冲控制得到了使其渐近稳定到原先不稳定的正平衡点的充分条件,使食饵密度和捕食者密度保持在一个定数附近并给出了生态解释.     

Simulation of First-Passage Times for Alternating Brownian Motions

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by an alternating renewal process. Bounds to the first-passage-time density and distribution function are obtained, and a simulation procedure to estimate first-passage-time densities is constructed. Examples of applications to problems in environmental sciences and mathematical finance are also provided.AMS 2000 Subject Classification: 60J65, 60G40, 93E30     

On the Generalized Telegraph Process with Deterministic Jumps

We consider a semi-Markovian generalization of the integrated telegraph process subject to jumps. It describes a motion on the real line characterized by two alternating velocities with opposite directions, where a jump along the alternating direction occurs at each velocity reversal. We obtain the formal expressions of the forward and backward transition densities of the motion. We express them as series in the case of Erlang-distributed random times separating consecutive jumps. Furthermore, a closed form of the transition density is given for exponentially distributed times, with constant jumps and random initial velocity. In this case we also provide mean and variance of the process, and study the limiting behaviour of the probability law, which leads to a mixture of three Gaussian densities.     

Simultaneous Packing and Covering in the Euclidean Plane

 In this article we study the simultaneous packing and covering constants of two-dimensional centrally symmetric convex domains. Besides an identity result between translative case and lattice case and a general upper bound, exact values for some special domains are determined. Similar to Mahler and Reinhardt’s result about packing densities, we show that the simultaneous packing and covering constant of an octagon is larger than that of a circle. (Received 17 January 2001; in revised form 13 July 2001)     

Smooth interface in a two-component Stokes flow

The problem considered is that of evolution of the free boundary Γ(t) separating two immiscible viscous fluids with different constant densities and viscosities. The motion is described by the Stokes equations driven by the gravity force. We prove the existence of classical solutions for small timet and establish that the free boundary Γ(t)∈C ^l+2 (l>0 is an arbitrary non-integer number)     

A time-delay model for the effect of toxicant in a single species growth with stage-structure

In this paper, we investigate a single-species growth model with stage-structure consisting of immature and mature stages for the effects of toxicants with constant maturation time-delay. We study the dynamics of our model in three cases: an instantaneous emission of toxicant, a constant emission of toxicant, and a periodic emission of toxicant into the environment. We present results on positivity and boundedness of all solutions under appropriate conditions. The model equations are analyzed mathematically with regard to the nature of equilibria and their stabilities using the theory of nonlinear differential equations and computer simulations. It is shown that under suitable conditions, there exists a globally asymptotically stable positive equilibrium. It is concluded from the analysis that as the concentration of toxicant in the environment increases, equilibrium densities of both immature and mature populations decrease. It is also noted that the effects of toxicants are more on the equilibrium level of immature population in comparison to the mature population.     

Effect of cross-velocity on the stability of superposed fluids

In the present paper we discuss the stability of the interface between two layers of incompressible and inviscid fluids of different but constant densities, streaming in different directions. The velocities in the different directions of the two fluid layers give rise to the concept of cross-velocity. We show that it destabilizes the interface while ifρ and U are continuous functions then it has stabilizing effect.     

Solvability of the system of equations of one-dimensional motion of a heat-conducting two-phase mixture

We prove the local solvability of the initial boundary-value problem for the system of equations of one-dimensional nonstationary motion of a heat-conducting two-phase mixture (gas plus solid particles). For the case in which the real densities of the phases are constant, we establish the solvability “in the large” with respect to time.