It is well known that various characteristics in risk and queuing process can be formulated as Markov Renewal function. We study the max-position of finitely many Markov Renewal Reward process with countable state space. We define Markov Renewal equation associated with max-posed process. The solutions of the Markov Renewal Reward equation are derived and the asymptotic behaviors of the equatio...

Abstract. The question about the existence and characterization of bounded solutions to linear functional-differential equations with both advanced and delayed arguments was posed in early 1970s by T. Kato in connection with the analysis of the pantograph equation, y(x) = ay(qx) + by(x). In the present paper, we answer this question for the balanced generalized pantograph equation of the form −...

Abstract We consider a nonlinear parabolic equation in one space variable, satisfying a three point boundary condition, such as the heat equation when the temperature at the end is controlled by a sensor at the the point η. We show that the integral solution, in the space of continuous functions satisfying the boundary values, converges to the equilibrium solution. This answers a question which...

In this paper, we study a system of equations that is known to extend Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergencefree. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of both controlling the nonlinear terms, and being useful at the time-discrete level. We address q...

The inclusion of steric effects is important when determining the electrostatic potential near a solute surface. We consider a modified form of the Poisson-Boltzmann equation, often called the Poisson-Bikerman equation, in order to model these effects. The modifications lead to bounded ionic concentration profiles and are consistent with the Poisson-Boltzmann equation in the limit of zero-size ...

In [2], F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard’s type, implying that the Cauch...

We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the “KdV-KdV” system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical K...

Hydrographic data, be it observational or averaged data, contain substantial regions having vertical density inversions. A new analytical conserved adjustment scheme has been developed on the base of conservation of heat, salt, and static stability for the whole water column with a predetermined (T, S) adjustment ratio. A set of well-posed combined linear and nonlinear algebraic equations has b...

We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. This follows a local energy decay result for the Kerr space-time obtained in the earlier work [23] and uses the techniques and results from [13] by the author and collaborator...

A kth-order linear difference equation with constant coefficients subject to boundary conditions is considered. A necessary and sufficient condition for the existence of a unique solution for such a boundary value problem is established. The condition established answers a fundamental question for well-posedness and can be easily applied using a simple and computationally tractable algorithm th...