In this work, traveling wave solutions (TWS) of a diffusive SIS epidemic model incorporating infection age structure and a general nonlinear incidence function are investigated. Through analysis of the associated differential system, the basic reproduction number R-0 is identified as the fundamental threshold parameter: when R-0 <= 1, disease invasion is prevented and no nontrivial wave emerges, whereas for R-0 > 1, the dynamics are characterized by a strictly positive minimal wave speed c & lowast; > 0. By employing spectral methods together with rigorously constructed upper and lower solutions, it is demonstrated that monotone waves connecting the disease free and endemic equilibria exist if and only if the propagation speed satisfies c >= c(& lowast;). Moreover, such waves are shown not to occur for 0 < c < c(& lowast;). Numerical simulations, formulated through phase plane trajectories and traveling wave profiles, are presented to validate the theoretical prediction of a sharp threshold at c = c(& lowast;).
This study identifies all Fibonacci numbers that can be expressed as the sum of two Jacobsthal numbers and all Jacobsthal numbers that can be expressed as the sum of two Fibonacci numbers. More precisely, we identify every non-negative integer solution (a, b, c) of the Diophantine equations Fa + Fb = Jcand Ja + Jb = Fc, where {Fc}c >= 0 and {Jc}c >= 0 are the sequences of Fibonacci and Jacobsthal numbers, respectively. An adaptation of Baker's theorem for linear forms in logarithms and Dujella and Peth & odblac;'s reduction method confirms our main results.
This study investigates the behavior of blood flow in the Left Coronary Artery (LCA) experiencing symmetrical narrowing, focusing on three stenosis geometries: triangular, trapezoidal, and overlapping (W-shape). It aims to develop a mathematical model of post-stenotic flow, assess the effectiveness of the Finite Volume Method (FVM), and analyze how stenosis shape and severity affect velocity and pressure. The governing equations of fluid motion are solved using FVM for spatial discretization and the SIMPLE algorithm to compute flow variables. Results show that FVM accurately simulates blood dynamics in narrowed arterial regions. Notably, when stenosis exceeds 50%, flow velocity increases significantly, reaching a peak at 75% narrowing. This condition also corresponds to a sharp pressure drop, especially in the trapezoidal model, indicating a higher potential for vascular damage and plaque accumulation. These changes in hemodynamic behavior highlight the critical role of stenosis geometry in altering blood flow. Therefore, understanding the influence of narrowing shape and severity is essential for clinical assessment and early diagnosis of coronary artery disease.
The present study numerically investigates the influence of thermal radiation and chemical reaction on thermosolutal mixed convection in a vertical pipe embedded in a porous medium, focusing on air water systems, which are directly applicable in technologies such as humidification-dehumidification desalination units and industrial cooling towers. The flow dynamics are modeled using the non Darcy Brinkman Forchheimer (NDBF) extended framework. The flow is driven by a combination of buoyancy forces arising from temperature and solute concentration gradients, along with an external pressure gradient. The governing coupled differential equations are solved using the Chebyshev spectral collocation method for high accuracy and spectral convergence. The results demonstrate that both the thermal radiation parameter (R) and chemical reaction parameter (gamma) significantly affect the velocity, temperature, and concentration profile of an air-water system. According to our findings, 'R' has a substantial effect on the instability of the fluid flow mechanism. In a Darcy porous media, where the Darcy number ranges from 10-5 to 10-2, the Prandtl number is taken as Pr = 0.71 for air and is Pr = 7 for water, it has been observed that the point of inflection arises faster in radiative flow than in non radiative flow with change of radiation parameter from 1 to 3 and subsequently to 5. The radiation parameter (R) leads to a decrease in temperature profile due to enhanced radiative heat loss, while it causes an increase in concentration profile. Additionally, as the chemical reaction parameter increases, the concentration profile diminishes due to species consumption. A similar suppressive effect on concentration is observed with higher Schmidt number (Sc), which indicates reduced mass diffusivity.
In this paper we consider the Cauchy problem for the second-order polyharmonic equation in an unbounded domain D, where boundary data are given on a part of boundary. The goal is to reconstruct a function v(eta) in D based on the given values of v, its Laplacian, and their normal derivatives. This is the ill-posed inverse problem, hence we use Carleman-type integral representations and stability estimates to ensure well-posed approximations. We construct the Carleman function and prove key inequalities governing its behavior. Additionally, Lavrent'ev regularization is applied to construct an approximate solution. We establish a regularized solution of the Cauchy problem for the biharmonic equation in an unbounded domain. These results provide a foundation for stable reconstruction methods for polyharmonic functions in certain classes of unbounded domains.
