Mathematical Methods in the Applied Sciences最新文献

This paper investigates the Cauchy problems for a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system via Riemannian invariants. Based on the first a priori estimate of the solutions, the second a priori estimate of the derivation of the solutions, and the third a priori estimate of the continuous mould of the first-order partial derivatives of the solutions to quasilinear hyperbolic system, a lower bound estimate of classical solutions to the Cauchy problems for a hyperbolic Monge–Ampère equation is derived.

In this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau–Korteweg De Vries-regularized long wave (Rosenau-KdV-RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization. After the time discretization, we have used polynomial scaling functions for the discretization of the spatial variable. These two discretizations give us the desired discrete system of equations to obtain numerical solutions. We further derive an error estimate for the proposed method. We have applied the proposed method to Rosenau-KdV, Rosenau-RLW, and Rosenau-KdV-RLW equations and used error norms to examine the accuracy and reliability of the presented method. Also, to enhance accuracy of the results, we utilize Richardson extrapolation. The comparisons with the analytical solution and earlier studies that use different methods indicate that the proposed method is accurate and reliable.

We analyze the generalized Hamiltonian structure of a system of first-order ordinary differential equations for the Jenner et al. system (Letters in Biomathematics 5 (2018), no. S1, S117–S136). The system of equations is used for modeling the interaction of an oncolytic virus with a tumor cell population. Our analysis is based on the existence of a Jacobi last multiplier and a time-dependent first integral. Suitable conditions on the model parameters allow for the reduction of the problem to a planar system of equations, and the time-dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows is also investigated using the symplectic and cosymplectic methods.

This paper studies quasi-sure exponential of triangular stochastic differential equations driven by $��G�$-Brownian motion ($��G�$-SDEs, in short) with the help of the stability of each diagonal subsystems by exponential martingale inequality and $��G�$-stochastic analysis techniques. This result allows us to study the full-order filtering problem of the stochastic systems driven $��G�$-Brownian motion.

This paper investigates a pursuit-evasion model with prey-taxis and indirect predator-taxis

The study of this article deals with the controllability results for time-varying fractional dynamical systems in terms of Caputo-type fractional derivatives having a prescribed or predetermined control. We demonstrate the controllability results for time-varying linear fractional dynamical systems using Gramian technique and fractional calculus. Additionally, we explore the controllability results for semi-linear and nonlinear fractional dynamical systems through the fixed point techniques. Several numerical examples are illustrated to validate the theoretical results.

We employ the theory of asymptotic homogenization (AH) to study the elasto-plastic behavior of a composite medium comprising two solid phases, separated by a sharp interface and characterized by mechanical properties, such as elastic coefficients and “initial yield stresses” (i.e., a threshold stress above which remodeling is triggered), that may differ up to several orders of magnitude. We speak of “plastic” behavior because we have in mind a material behavior that, to a certain extent, resembles plasticity, although, for biological systems, it embraces a much wider class of inelastic phenomena. In particular, we are interested in studying the influence of gradient effects in the remodeling variable on the homogenized mechanical properties of the composite. The jump of the mechanical properties from one phase to the other makes the composite highly heterogeneous and calls for the determination of effective properties, that is, properties that are associated with a homogenized “version” of the original composite, and that are obtained through a suitable averaging procedure. The determination of the effective properties results convenient, in particular, when it comes to the multiscale description of inelastic processes, such as remodeling in soft or hard tissues, like bones. To accomplish this task with the aid of AH, we assume that the length scale over which the heterogeneities manifest themselves is several orders of magnitude smaller than the characteristic length scale of the composite as a whole. We identify both a fine-scale problem and a coarse-scale problem, each of which characterizes the elasto-plastic dynamics of the composite at the corresponding scale, and we discuss how they are reciprocally coupled through a transfer of information from one scale to the other. In particular, we highlight how the coarse-scale plastic distortions influence the fine-scale problem. Moreover, in the limit of negligible hysteresis effects, we individuate two viscoplastic effective coefficients that encode the information of the two-scale nature of the composite medium in the upscaled equations. Finally, to deal with a case study tractable semi-analytically, we consider a multilayered composite material with an initial yield stress that is constant in each phase. Such investigation is meant to contribute to the constitution of a robust framework for devising the effective properties of hierarchical biological media.

We are concerned with the Kirchhoff problem

For an inverse coefficient problem of determining a state-varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an arbitrarily chosen subdomain over a time interval. The proof is based on Carleman estimates with different norms.

Tuberculosis (TB) caused by Mycobacterium tuberculosis (Mtb) is a devastating and rapidly spreading disease. Despite years of scientific research and numerous efforts, it is still a major and resurgent health problem worldwide, with high mortality rates. Added to the concern is that TB persists as a latent infection, an occult face of TB, that becomes a potential reservoir for active tuberculosis. Since latent TB-infected patients may eventually advance to the active form of TB, an accurate diagnosis and effective treatment of latent tuberculosis are essential for TB control. Latent tuberculosis infection (LTBI) treatment is a prominent component of TB control in low-prevalence countries like the United States; however, its implication in high-incidence countries like India is still challenging. Therefore, the present study aimed to evaluate the impact of implementing diagnosis and treatment of LTBI in high-incidence countries using a mathematical model-based approach. Through our model, we predicted the incidence rate based on the current treatment regimen in India for the year 2035, which is one of the milestones of WHO for a substantial reduction in TB incidence. We observed demographic variability in the effects of various parameters on the TB incidence rate. Finally, we formulated the putative treatment strategies to reduce the TB burden in high-incidence scenarios. Further, we estimated the impact of these proposed treatment strategies on the drug-resistant population in high-incidence scenarios. The model predictions suggested molding the current treatment strategies and focused implementation of LTBI diagnosis and treatment in high-incidence scenarios.