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On stochastic properties of past varentropy with applications Appl. Math. (IF 0.7) Pub Date : 2024-03-11 Akash Sharma, Chanchal Kundu
To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose
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Ridge estimation of covariance matrix from data in two classes Appl. Math. (IF 0.7) Pub Date : 2024-02-22
Abstract This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model
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Multi-type synchronization of impulsive coupled oscillators via topology degree Appl. Math. (IF 0.7) Pub Date : 2024-02-19
Abstract The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way.
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Exploring the impact of post-training rounding in regression models Appl. Math. (IF 0.7) Pub Date : 2024-02-15
Abstract Post-training rounding, also known as quantization, of estimated parameters stands as a widely adopted technique for mitigating energy consumption and latency in machine learning models. This theoretical endeavor delves into the examination of the impact of rounding estimated parameters in key regression methods within the realms of statistics and machine learning. The proposed approach allows
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Identification of source term in a nonlinear degenerate parabolic equation with memory Appl. Math. (IF 0.7) Pub Date : 2024-02-07
Abstract In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers’ type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability
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A balanced finite-element method for an axisymmetrically loaded thin shell Appl. Math. (IF 0.7) Pub Date : 2024-01-30 Norbert Heuer, Torsten Linss
We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.
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Development of small and large compressive pulses in two-phase flow Appl. Math. (IF 0.7) Pub Date : 2024-01-23 Nishi Deepa Palo, Jasobanta Jena, Meera Chadha
The evolutions of small and large compressive pulses are studied in a two-phase flow of gas and dust particles with a variable azimuthal velocity. The method of relatively undistorted waves is used to study the mechanical pulses of different types in a rotational, axisymmetric dusty gas. The results obtained are compared with that of nonrotating medium. Asymptotic expansion procedure is used to discuss
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Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph Appl. Math. (IF 0.7) Pub Date : 2024-01-10 Bijoya Bardhan, Mausumi Sen, Debashish Sharma
In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme
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Homogenization of Monotone Parabolic Problems with an Arbitrary Number of Spatial and Temporal Scales Appl. Math. (IF 0.7) Pub Date : 2023-12-18 Tatiana Danielsson, Liselott Flodén, Pernilla Johnsen, Marianne Olsson Lindberg
We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter ε. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems.
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Strong Convergence for Weighted Sums of WOD Random Variables and its Application in the EV Regression Model Appl. Math. (IF 0.7) Pub Date : 2023-12-08 Liwang Ding, Caoqing Jiang
The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further investigate the strong consistency of the least squares estimator in EV regression model for WOD random variables. A simulation study is carried out to confirm the theoretical results.
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A New Block Triangular Preconditioner for Three-by-Three Block Saddle-Point Problem Appl. Math. (IF 0.7) Pub Date : 2023-12-07 Jun Li, Xiangtuan Xiong
In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the
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Relaxation-Time Limits of Global Solutions in Full Quantum Hydrodynamic Model for Semiconductors Appl. Math. (IF 0.7) Pub Date : 2023-11-11 Sungjin Ra, Hakho Hong
This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in ℝ3, we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data
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Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction Appl. Math. (IF 0.7) Pub Date : 2023-11-08 Michael Ruderman
The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals
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A continuum of path-dependent equilibrium solutions induced by sticky expectations Appl. Math. (IF 0.7) Pub Date : 2023-11-06 Pavel Krejčí, Eyram Kwame, Harbir Lamba, Dmitrii Rachinskii, Andrei Zagvozdkin
We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational
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On the Stability Analysis of Darboux Problem on Both Bounded and Unbounded Domains Appl. Math. (IF 0.7) Pub Date : 2023-11-03 Canan Çelik, Faruk Develi
In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results.
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Continuity of the non-convex play operator in the space of rectifiable curves Appl. Math. (IF 0.7) Pub Date : 2023-10-25 Jana Kopfová, Vincenzo Recupero
We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the BV-norm and to the BV-strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent
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On forward and inverse uncertainty quantification for a model for a magneto mechanical device involving a hysteresis operator Appl. Math. (IF 0.7) Pub Date : 2023-10-12 Olaf Klein
Modeling real world objects and processes one may have to deal with hysteresis effects but also with uncertainties. Following D. Davino, P. Krejčí, and C. Visone (2013), a model for a magnetostrictive material involving a generalized Prandtl-Islilinskiĭ-operator is considered here. Using results of measurements, some parameters in the model are determined and inverse Uncertainty Quantification (UQ)
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Anisotropic viscoelastic body subjected to the pulsating load Appl. Math. (IF 0.7) Pub Date : 2023-09-14 Jozef Sumec, Mária Minárová, L’uboš Hruštinec
Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later
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Density deconvolution with associated stationary data Appl. Math. (IF 0.7) Pub Date : 2023-09-03 Le Thi Hong Thuy, Cao Xuan Phuong
We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions
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Inexact Newton-type method for solving large-scale absolute value equation Ax − ∣x∣ = b Appl. Math. (IF 0.7) Pub Date : 2023-08-31 Jingyong Tang
Newton-type methods have been successfully applied to solve the absolute value equation Ax − ∣x∣ = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the
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A survey of some recent results on Clifford algebras in $${\mathbb{R}^4}$$ Appl. Math. (IF 0.7) Pub Date : 2023-08-10 Drahoslava Janovská, Gerhard Opfer
We will study applications of numerical methods in Clifford algebras in \({\mathbb{R}^4}\), in particular in the skew field of quaternions, in the algebra of coquaternions and in the other nondivision algebras in \({\mathbb{R}^4}\). In order to gain insight into the multidimensional case, we first consider linear equations in quaternions and coquaternions. Then we will search for zeros of one-sided
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Convergence of a proposed adaptive WENO scheme for Hamilton-Jacobi equations Appl. Math. (IF 0.7) Pub Date : 2023-08-09 Wonho Han, Kwangil Kim, Unhyok Hong
We study high-order numerical methods for solving Hamilton-Jacobi equations. Firstly, by introducing new clear concise nonlinear weights and improving their convex combination, we develop WENO schemes of Zhu and Qiu (2017). Secondly, we give an algorithm of constructing a convergent adaptive WENO scheme by applying the simple adaptive step on the proposed WENO scheme, which is based on the introduction
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Fourier diffraction theorem for the tensor fields Appl. Math. (IF 0.7) Pub Date : 2023-08-09 Alexander Leonidovich Balandin
The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered a useful tool for studying
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Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory Appl. Math. (IF 0.7) Pub Date : 2023-07-21 Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht, Thibaut Weller
We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical
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Global existence of smooth solutions for the compressible viscous fluid flow with radiation in $${\mathbb{R}^3}$$ Appl. Math. (IF 0.7) Pub Date : 2023-06-13 Hyejong O, Hakho Hong, Jongsung Kim
This paper is concerned with the 3-D Cauchy problem for the compressible viscous fluid flow taking into account the radiation effect. For more general gases including ideal polytropic gas, we prove that there exists a unique smooth solutions in [0, ∞), provided that the initial perturbations are small. Moreover, the time decay rates of the global solutions are obtained for higher-order spatial derivatives
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A new approach to solving a quasilinear boundary value problem with p-Laplacian using optimization Appl. Math. (IF 0.7) Pub Date : 2023-06-09 Michaela Bailová, Jiří Bouchala
We present a novel approach to solving a specific type of quasilinear boundary value problem with p-Laplacian that can be considered an alternative to the classic approach based on the mountain pass theorem. We introduce a new way of proving the existence of nontrivial weak solutions. We show that the nontrivial solutions of the problem are related to critical points of a certain functional different
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A generalization of the classical Euler and Korteweg fluids Appl. Math. (IF 0.7) Pub Date : 2023-05-29 Kumbakonam Ramamani Rajagopal
The aim of this short paper is threefold. First, we develop an implicit generalization of a constitutive relation introduced by Korteweg (1901) that can describe the phenomenon of capillarity. Second, using a sub-class of the constitutive relations (implicit Euler equations), we show that even in that simple situation more than one of the members of the sub-class may be able to describe one or a set
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Bifurcation analysis of macroscopic traffic flow model based on the influence of road conditions Appl. Math. (IF 0.7) Pub Date : 2023-05-18 Wenhuan Ai, Ting Zhang, Dawei Liu
A macroscopic traffic flow model considering the effects of curves, ramps, and adverse weather is proposed, and nonlinear bifurcation theory is used to describe and predict nonlinear traffic phenomena on highways from the perspective of global stability of the traffic system. Firstly, the stability conditions of the model shock wave were investigated using the linear stability analysis method. Then
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An Entropy Stable Finite Volume Method for a Compressible Two Phase Model Appl. Math. (IF 0.7) Pub Date : 2023-03-29 Eduard Feireisl, Mădălina Petcu, Bangwei She
We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory.
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A Tight Bound of Modified Iterative Hard Thresholding Algorithm for Compressed Sensing Appl. Math. (IF 0.7) Pub Date : 2023-03-21 Jinyao Ma, Haibin Zhang, Shanshan Yang, Jiaojiao Jiang
We provide a theoretical study of the iterative hard thresholding with partially known support set (IHT-PKS) algorithm when used to solve the compressed sensing recovery problem. Recent work has shown that IHT-PKS performs better than the traditional IHT in reconstructing sparse or compressible signals. However, less work has been done on analyzing the performance guarantees of IHT-PKS. In this paper
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Inverse Rate-Dependent Prandtl-Ishlinskii Operators and Applications Appl. Math. (IF 0.7) Pub Date : 2023-02-09 Mohammad Al Janaideh, Pavel Krejčí, Giselle Antunes Monteiro
In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent
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The Descent Algorithms for Solving Symmetric Pareto Eigenvalue Complementarity Problem Appl. Math. (IF 0.7) Pub Date : 2023-02-03 Lu Zou, Yuan Lei
For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the
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Spatial decay estimates for the Forchheimer fluid equations in a semi-infinite cylinder Appl. Math. (IF 0.7) Pub Date : 2022-12-07 Xuejiao Chen, Yuanfei Li
The spatial behavior of solutions is studied in the model of Forchheimer equations. Using the energy estimate method and the differential inequality technology, exponential decay bounds for solutions are derived. To make the decay bounds explicit, we obtain the upper bound for the total energy. We also extend the study of spatial behavior of Forchheimer porous material in a saturated porous medium
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Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI Appl. Math. (IF 0.7) Pub Date : 2022-12-06 Alexandros Markopoulos, Petr Beremlijski, Oldřich Vlach, Marie Sadowská
The present paper deals with the numerical solution of 3D shape optimization problems in frictional contact mechanics. Mathematical modelling of the Coulomb friction problem leads to an implicit variational inequality which can be written as a fixed point problem. Furthermore, it is known that the discretized problem is uniquely solvable for small coefficients of friction. Since the considered problem
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Finite time stability and relative controllability of second order linear differential systems with pure delay Appl. Math. (IF 0.7) Pub Date : 2022-11-30 Mengmeng Li, Michal Fečkan, JinRong Wang
We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally
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Global bifurcations in a dynamical model of recurrent neural networks Appl. Math. (IF 0.7) Pub Date : 2022-11-18 Anita Windisch, Péter L. Simon
The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf
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Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum Appl. Math. (IF 0.7) Pub Date : 2022-10-27 Huanyuan Li
This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the
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Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions Appl. Math. (IF 0.7) Pub Date : 2022-10-18 Deepak Kumar, Virendra Kumar, Laxminarayan Das
In this paper, we have determined the sharp lower and upper bounds on the fourth-order Hermitian-Toeplitz determinant for starlike functions with real coefficients. We also obtained the sharp bounds on the Hermitian-Toeplitz determinants of inverse and logarithmic coefficients for starlike functions with complex coefficients. Sharp bounds on the modulus of differences and difference of moduli of logarithmic
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Global regularity for the 3D inhomogeneous incompressible Navier-Stokes equations with damping Appl. Math. (IF 0.7) Pub Date : 2022-10-11 Kwang-Ok Li, Yong-Ho Kim
This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible
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On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks Appl. Math. (IF 0.7) Pub Date : 2022-10-05 Ctirad Matonoha, Štěpán Papáček, Volodymyr Lynnyk
We develop and test a relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both the methods, being (i) the standard quasi-steady-state approximation method, and (ii) the novel so-called delayed quasi-steady-state approximation method, firstly proposed by Vejchodský (2014), are extensively presented. Both theoretical
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Solving intuitionistic fuzzy multi-objective linear programming problem and its application in supply chain management Appl. Math. (IF 0.7) Pub Date : 2022-09-15 Hassan Hassanpour, Elham Hosseinzadeh, Mahsa Moodi
The aim of this paper is solving an intuitionistic fuzzy multi-objective linear programming problem containing intuitionistic fuzzy parameters, intuitionistic fuzzy maximization/minimization, and intuitionistic fuzzy constraints. To do this, a linear ranking function is used to convert the intuitionistic fuzzy parameters to crisp ones first. Then, linear membership and non-membership functions are
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A General Decay Estimate for a Finite Memory Thermoelastic Bresse System Appl. Math. (IF 0.7) Pub Date : 2022-07-25 Cyril Dennis Enyi, Soh Edwin Mukiawa
This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that
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Non-linear Chandrasekhar-Bénard convection in temperature-dependent variable viscosity Boussinesq-Stokes suspension fluid with variable heat source/sink Appl. Math. (IF 0.7) Pub Date : 2022-07-01 Nagasundar Kavitha, Agrahara Sanjeevmurthy Aruna, MKoppalu Shankarappa Basavaraj, Venkatesh Ramachandramurthy
The generalized Lorenz model for non-linear stability of Rayleigh-Bénard magneto-convection is derived in the present paper. The Boussinesq-Stokes suspension fluid in the presence of variable viscosity (temperature-dependent viscosity) and internal heat source/sink is considered in this study. The influence of various parameters like suspended particles, applied vertical magnetic field, and the temperature-dependent
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The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in Lr-framework Appl. Math. (IF 0.7) Pub Date : 2022-06-28 Tomáš Neustupa
We deal with the steady Stokes problem, associated with a flow of a viscous incompressible fluid through a spatially periodic profile cascade. Using the reduction to domain Ω, which represents one spatial period, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves Γ− and Γ+ (lower and upper parts of ∂Ω), the Dirichlet boundary conditions
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On the Maxwell-wave equation coupling problem and its explicit finite-element solution Appl. Math. (IF 0.7) Pub Date : 2022-06-22 Larisa Beilina, Vitoriano Ruas
It is well known that in the case of constant dielectric permittivity and magnetic permeability, the electric field solving the Maxwell’s equations is also a solution to the wave equation. The converse is also true under certain conditions. Here we study an intermediate situation in which the magnetic permeability is constant and a region with variable dielectric permittivity is surrounded by a region
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Tight bounds for the dihedral angle sums of a pyramid Appl. Math. (IF 0.7) Pub Date : 2022-06-21 Sergey Korotov, Lars Fredrik Lund, Jon Eivind Vatne
We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval (3π, 5π). Moreover, for any number in (3π, 5π) there exists a pyramid whose dihedral angle sum is equal to this number, which means that the lower and upper bounds are tight. Furthermore, the improved (and tight) upper bound 4π is derived for the class of pyramids with parallelogramic
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Multiscale homogenization of nonlinear hyperbolic-parabolic equations Appl. Math. (IF 0.7) Pub Date : 2022-06-17 Abdelhakim Dehamnia, Hamid Haddadou
The main purpose of the present paper is to study the asymptotic behavior (when ε → 0) of the solution related to a nonlinear hyperbolic-parabolic problem given in a periodically heterogeneous domain with multiple spatial scales and one temporal scale. Under certain assumptions on the problem’s coefficients and based on a priori estimates and compactness results, we establish homogenization results
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Flocking analysis for a generalized Motsch-Tadmor model with piecewise interaction functions and processing delays Appl. Math. (IF 0.7) Pub Date : 2022-06-14 Yipeng Chen, Yicheng Liu, Xiao Wang
In this paper, a generalized Motsch-Tadmor model with piecewise interaction functions and fixed processing delays is investigated. According to functional differential equation theory and correlation properties of the stochastic matrix, we obtained sufficient conditions for the system achieving flocking, including an upper bound of the time delay parameter. When the parameter is less than the upper
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A free boundary problem for some modified predator-prey model in a higher dimensional environment Appl. Math. (IF 0.7) Pub Date : 2022-06-14 Hongmei Cheng, Qinhe Fang, Yang Xia
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to
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Absolute value equations with tensor product structure: Unique solvability and numerical solution Appl. Math. (IF 0.7) Pub Date : 2022-06-10 Somayeh Mollahsani, Fatemeh Panjeh Ali Beik
We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence
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Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis Appl. Math. (IF 0.7) Pub Date : 2022-06-06 Bohumír Bastl, Marek Brandner, Kristýna Slabá, Eva Turnerová
In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged Navier-Stokes equations closed by the SST k-ω turbulence model. The stabilization scheme is constructed such that it is consistent in the sense used in the finite element method, artificial diffusion is added only in the direction of convection and it is based
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On a new computational algorithm for impacts of elastic bodies Appl. Math. (IF 0.7) Pub Date : 2022-05-30 Hynek Štekbauer, Ivan Němec, Rostislav Lang, Daniel Burkart, Jiří Vala
Computational modelling of contact problems is still one of the most difficult aspects of non-linear analysis in engineering mechanics. The article introduces an original efficient explicit algorithm for evaluation of impacts of bodies, satisfying the conservation of both momentum and energy exactly. The algorithm is described in its linearized 2-dimensional formulation in details, as open to numerous
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Analysis of pattern formation using numerical continuation Appl. Math. (IF 0.7) Pub Date : 2022-05-02 Vladimír Janovský
The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter L, which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to
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Global attractors for a tropical climate model Appl. Math. (IF 0.7) Pub Date : 2022-04-08 Pigong Han, Keke Lei, Chenggang Liu, Xuewen Wang
This paper is devoted to the global attractors of the tropical climate model. We first establish the global well-posedness of the system. Then by studying the existence of bounded absorbing sets, the global attractor is constructed. The estimates of the Hausdorff dimension and of the fractal dimension of the global attractor are obtained in the end.
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Resilient asynchronous primal Schur method Appl. Math. (IF 0.7) Pub Date : 2022-04-05 Guillaume Gbikpi-Benissan, Frédéric Magoulès
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated
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On Surrogate Learning for Linear Stability Assessment of Navier-Stokes Equations with Stochastic Viscosity Appl. Math. (IF 0.7) Pub Date : 2022-03-01 Bedřich Sousedík, Howard C. Elman, Kookjin Lee, Randy Price
We study linear stability of solutions to the Navier-Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While
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On the Parameter in Augmented Lagrangian Preconditioning for Isogeometric Discretizations of the Navier-Stokes Equations Appl. Math. (IF 0.7) Pub Date : 2022-02-17 Jiří Egermaier, Hana Horníková
In this paper, we deal with the optimal choice of the parameter γ for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the
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Low Mach Number Limit of a Compressible Euler-Korteweg Model Appl. Math. (IF 0.7) Pub Date : 2022-02-16 Yajie Wang, Jianwei Yang
This article deals with the low Mach number limit of the compressible Euler-Korteweg equations. It is justified rigorously that solutions of the compressible Euler-Korteweg equations converge to those of the incompressible Euler equations as the Mach number tends to zero. Furthermore, the desired convergence rates are also obtained.
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Continuous Dependence and General Decay of Solutions for a Wave Equation with a Nonlinear Memory Term Appl. Math. (IF 0.7) Pub Date : 2022-02-08 Doan Thi Nhu Quynh, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long
We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution
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Existence and Uniqueness for a Two-Dimensional Ventcel Problem Modeling the Equilibrium of a Prestressed Membrane Appl. Math. (IF 0.7) Pub Date : 2022-01-26 Antonio Greco, Giuseppe Viglialoro
This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that one of the boundary conditions involves second order differentiation along the boundary. Under suitable assumptions on the data, we first give the definition of a weak solution, and then we prove that the problem is uniquely solvable. We also consider a