Authors:Alaaeddine Hammoudi, Oana Iosifescu, Martial Bernoux Pages: 771 - 793 Abstract: Analysis and Applications, Volume 15, Issue 06, Page 771-793, November 2017. The aim of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction–diffusion–advection system with a quadratic reaction term. This is a spatial version of Modeling Organic changes by Micro-Organisms of Soil model, recently introduced by M. Pansu and his group. We show here that for any nonnegative initial condition, there exists a unique nonnegative weak solution. Moreover, if we assume time periodicity of model entries, taking into account seasonal effects, we prove existence of a minimal and a maximal periodic weak solution. In a particular case, these two solutions coincide and they become a global attractor of any bounded solution of the periodic system. Citation: Analysis and Applications PubDate: 2017-08-03T03:11:49Z DOI: 10.1142/S0219530516500081

Authors:Seung-Yeal Ha, Se Eun Noh, Jinyeong Park Pages: 837 - 861 Abstract: Analysis and Applications, Volume 15, Issue 06, Page 837-861, November 2017. We study the dynamic interplay between inertia and heterogeneous dynamics in an ensemble of Kuramoto oscillators. When external fields and internal forces are exerted on a system of Kuramoto oscillators, each oscillator has its own distinct dynamics, so that there is no notion of collective dynamics in the ensemble, and complete synchronization is not observed in such systems. In this paper, we study a relaxed version of synchronization, namely the “practical synchronization”, of Kuramoto oscillators, emerging from the dynamic interplay between inertia and heterogeneous decoupled dynamics. We will show that for some class of initial configurations and parameters, the fluctuation of phases and frequencies around the average values will be proportional to the inverse of the coupling strength. We provide several numerical examples, and compare these with our analytical results. Citation: Analysis and Applications PubDate: 2017-08-03T03:11:53Z DOI: 10.1142/S0219530516500111

Authors:Francesco De Anna Pages: 863 - 913 Abstract: Analysis and Applications, Volume 15, Issue 06, Page 863-913, November 2017. The most established theory for modeling the dynamics of nematic liquid crystals is the celebrated Ericksen–Leslie system, which presents some major analytical challenges. We study a simplified version of the system, which still exhibits the major difficulties. We consider the density-dependent case and study the Cauchy problem in the whole space. We establish the global existence of solutions for small initial data by assuming only that the initial density is bounded and kept away far from vacuum, while the initial velocity and the gradient of the initial director field belong to certain critical Besov spaces. Under slightly more assumptions on the initial velocity and the director field, we also prove that the solutions are unique. Citation: Analysis and Applications PubDate: 2017-08-03T03:11:54Z DOI: 10.1142/S0219530516500172

Authors:Sibei Yang, Der-Chen Chang, Dachun Yang, Zunwei Fu Pages: 1 - 23 Abstract: Analysis and Applications, Ahead of Print. In this paper, by applying the well-known method for dealing with [math]-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and the Neumann boundary value problems of a class of Schrödinger equations, under the weak regularity assumption on the boundary of domains. As applications, the gradient estimates of these solutions in Lebesgue spaces and Lorentz spaces are obtained. Citation: Analysis and Applications PubDate: 2017-08-15T02:51:20Z DOI: 10.1142/S0219530517500142

Authors:Seung-Yeal Ha, Hwa Kil Kim, Jinyeong Park Pages: 1 - 39 Abstract: Analysis and Applications, Ahead of Print. The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity, 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle. Citation: Analysis and Applications PubDate: 2017-07-05T07:46:04Z DOI: 10.1142/S0219530517500130

Authors:Mourad E. H. Ismail, Ruiming Zhang Pages: 1 - 73 Abstract: Analysis and Applications, Ahead of Print. By applying an integral representation for [math], we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of [math]-functions and polynomials that naturally arise from combinatorics, analysis, and orthogonal polynomials corresponding to indeterminate moment problems. These functions include [math]-Bessel functions, the Ramanujan function, Stieltjes–Wigert polynomials, [math]-Hermite and [math]-Hermite polynomials, and the [math]-exponential functions [math], [math] and [math]. Their representations are in turn used to derive many new identities involving [math]-functions and polynomials. In this paper, we also present contour integral representations for the above mentioned functions and polynomials. Citation: Analysis and Applications PubDate: 2017-07-05T07:46:03Z DOI: 10.1142/S0219530517500129

Authors:Yulong Zhao, Jun Fan, Lei Shi Pages: 1 - 22 Abstract: Analysis and Applications, Ahead of Print. The ranking problem aims at learning real-valued functions to order instances, which has attracted great interest in statistical learning theory. In this paper, we consider the regularized least squares ranking algorithm within the framework of reproducing kernel Hilbert space. In particular, we focus on analysis of the generalization error for this ranking algorithm, and improve the existing learning rates by virtue of an error decomposition technique from regression and Hoeffding’s decomposition for U-statistics. Citation: Analysis and Applications PubDate: 2017-04-11T11:48:28Z DOI: 10.1142/S0219530517500063

Authors:Hai-Yang Jin, Zhi-An Wang Pages: 1 - 32 Abstract: Analysis and Applications, Ahead of Print. In this paper, we consider the following dual-gradient chemotaxis model ut = Δu −∇⋅ (χu∇v) + ∇⋅ (ξf(u)∇w),x ∈ Ω,t > 0, τ1vt = Δv + αu − βv, x ∈ Ω,t > 0, τ2wt = Δw + γu − δw, x ∈ Ω,t > 0, with [math] for [math] and [math] for [math], where [math] is a bounded domain in [math] with smooth boundary, [math] and [math]. The model was proposed to interpret the spontaneous aggregation of microglia in Alzheimer’s disease due to the interaction of attractive and repulsive chemicals released by the microglia. It has been shown in the literature that, when [math], the solution of the model with homogeneous Neumann boundary conditions either blows up or asymptotically decays to a constant in multi-dimensions depending on the sign of [math], which means there is no pattern formation. In this paper, we shall show as [math], the uniformly-in-time bounded global classical solutions exist in multi-dimensions and hence pattern formation can develop. This is significantly different from the results for the case [math]. We perform the numerical simulations to illustrate the various patterns generated by the model, verify our analytical results and predict some unsolved questions. Biological applications of our results are discussed and open problems are presented. Citation: Analysis and Applications PubDate: 2017-04-11T11:48:28Z DOI: 10.1142/S0219530517500087

Authors:Blanca Bujanda, José L. López, Pedro J. Pagola Pages: 1 - 14 Abstract: Analysis and Applications, Ahead of Print. We consider the incomplete gamma function [math] for [math] and [math]. We derive several convergent expansions of [math] in terms of exponentials and rational functions of [math] that hold uniformly in [math] with [math] bounded from below. These expansions, multiplied by [math], are expansions of [math] uniformly convergent in [math] with [math] bounded from above. The expansions are accompanied by realistic error bounds. Citation: Analysis and Applications PubDate: 2017-04-11T11:48:27Z DOI: 10.1142/S0219530517500099

Authors:Philippe G. Ciarlet, Cristinel Mardare Pages: 1 - 20 Abstract: Analysis and Applications, Ahead of Print. We recast the displacement-traction problem of the Kirchhoff–Love theory of linearly elastic plates as a boundary value problem with the bending moments and stress resultants inside the middle section of the plate as the sole unknowns, instead of the displacement field in the classical formulation. To this end, we show in particular how to recast the Dirichlet boundary conditions satisfied by the displacement field of the middle surface of a plate as boundary conditions satisfied by the bending moments and stress resultants. Citation: Analysis and Applications PubDate: 2017-04-11T11:48:27Z DOI: 10.1142/S0219530517500105

Authors:Arash Ghaani Farashahi Pages: 1 - 19 Abstract: Analysis and Applications, Ahead of Print. This paper introduces a unified approach to the abstract notion of relative Gabor transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let [math] be a locally compact group, [math] be a locally compact Abelian (LCA) group, and [math] be a continuous homomorphism. Let [math] be the semi-direct product of [math] and [math] with respect to [math], [math] be the canonical homogeneous space of [math], and [math] be the canonical relatively invariant measure on [math]. Then we present a unified harmonic analysis approach to the theoretical aspects of the notion of relative Gabor transform over the Hilbert function space [math]. Citation: Analysis and Applications PubDate: 2017-04-11T11:48:27Z DOI: 10.1142/S0219530517500075

Authors:Chundi Liu, Boyi Wang Pages: 1 - 23 Abstract: Analysis and Applications, Ahead of Print. Quasineutral limit for a model of three-dimensional Euler–Poisson system in half space with a boundary layer is studied. Based on the matched asymptotic expansion method of singular perturbation problem and the elaborate energy method, we prove that the quasineutral regime is the incompressible Euler equation. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S0219530517500051

Authors:Alberto Bressan, Yilun Jiang Pages: 1 - 25 Abstract: Analysis and Applications, Ahead of Print. The paper studies optimal strategies for a borrower who needs to repay his debt, in an infinite time horizon. An instantaneous bankruptcy risk is present, which increases with the size of the debt. This induces a pool of risk-neutral lenders to charge a higher interest rate, to compensate for the possible loss of part of their investment. Solutions are interpreted as Stackelberg equilibria, where the borrower announces his repayment strategy [math] at all future times, and lenders adjust the interest rate accordingly. This yields a highly non-standard problem of optimal control, where the instantaneous dynamics depend on the entire future evolution of the system. Our analysis shows the existence of optimal open-loop controls, deriving necessary conditions for optimality and characterizing possible asymptotic limits as [math]. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S0219530517500038

Authors:Xiaoping Zhai, Yongsheng Li, Wei Yan Pages: 1 - 43 Abstract: Analysis and Applications, Ahead of Print. In this paper, we investigate the Cauchy problem for the 3D viscous nonhomogeneous incompressible magnetohydrodynamic equations in critical Besov spaces. We aim at proving the local and global well-posedness for respectively large and small initial data having critical Besov regularity, without assumptions of small density variation. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S0219530517500014

Authors:Giovanni S. Alberti, Stephan Dahlke, Filippo De Mari, Ernesto De Vito, Stefano Vigogna Pages: 1 - 23 Abstract: Analysis and Applications, Ahead of Print. We study a family of coherent states, called Schrödingerlets, both in the continuous and discrete setting. They are defined in terms of the Schrödinger equation of a free quantum particle and some of its invariant transformations. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S021953051750004X