Article
Mathematics, Applied
Bin Qian
Summary: In this paper, a refined Hamilton's gradient estimate for the heat equation is presented, along with new Harnack inequalities and bounds of the associated heat kernels. Inspired by Yau's work, a generalized Li-Yau gradient estimate for the linear heat equation is obtained, extending some known results and generating new gradient estimates.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Dibyajyoti Hazarika, Jayanta Borah, Bhupendra Kumar Singh
Summary: In this article, we investigate the existence and controllability of mild solutions of nonlocal fractional dynamical system with almost sectorial operator. The system involves Caputo fractional derivative of order alpha is an element of (0, 1). The existence results are proved using fixed point theorems with suitable assumptions. Sufficient conditions for controllability are derived using appropriate control function via Leray-Schauder fixed point theorem.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Limin Zhu
Summary: This paper studies the inviscid compressible Cattaneo-Christov system in one-dimensional space. The iterative method is used to establish the local well-posedness of this system for large data in critical Besov spaces based on the L2 framework. Moreover, the global existence of a strong solution can be proved when the initial perturbation around a constant state is sufficiently small, using the renormalized energy method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Hualei Zhang
Summary: This paper studies the longtime behavior of the weakly coupled Euler-Bernoulli plate system with one structural damping. The energy decay rate of the system under certain conditions is analyzed.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Yinan Wang, Zhaowen Yan
Summary: In this paper, the (m,n)-order tau-function of the universal character hierarchy is investigated using the fermionic approach. The general tau-function for charged free fermions is presented, and soliton solutions of the UC hierarchy are discussed. Furthermore, the algebraic structure and properties of the BUC hierarchy are developed, and the polynomial tau-functions and extended formulas of the BUC and 2-component BUC hierarchies are analyzed. Rational solutions of the BUC hierarchy are derived, and it is shown that soliton solutions of the BUC hierarchy can be expressed as multiplication of Pfaffians.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Samer Dweik
Summary: In this paper, we consider a mass transportation problem in a two-dimensional region and aim to minimize the transportation cost by optimizing the free transport region. We study the regularity of the transport density on the boundary and prove the existence of an optimal set for shape optimization. Furthermore, we establish the regularity of the optimal set when the penalization term is given by the perimeter of the set.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Hong Rae Cho, Hyungwoon Koo, Young Joo Lee
Summary: In this study, we focus on the orthogonal complement of the polyanalytic Fock space to investigate the properties of dual Toeplitz operators. We characterize the zero sum of products of two dual Toeplitz operators with harmonic symbols. Our results extend several known results on the analytic Fock space to every polyanalytic Fock spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Yanqin Xiong, Guangping Hu
Summary: This paper investigates the problem of heteroclinic loop bifurcation by perturbing a class of Z(2)-equivariant quadratic switching systems with nilpotent singular points. It provides sufficient and necessary conditions for the occurrence of a heteroclinic loop, and finds the lower bound for the maximum number of limit cycles that bifurcate from the generalized heteroclinic loop.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Siqi Liu, Yang Liu, Yuan Zhang
Summary: We investigate the Cauchy problem of a fluid-particle interaction model with vacuum as far field density in R2. We establish a blowup criterion for the strong solution of the problem, which extends a previous result to the 2D case and is independent of the particle velocity and density.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Huda Alzaki, Jae-Cheon Joo
Summary: We investigate the use of the indicatrix of an invariant metric to rescale a sequence of biholomorphic maps and ensure the convergence of the rescaled sequence. We also define the maximal circularity function using the indicatrix of the Kobayashi-Royden metric, which indicates how close the domain is to a circular domain.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Andras Kroo
Summary: The goal of this paper is to establish that the square root of the Euclidean distance to the boundary is a universal measure for obtaining L-p Bernstein type inequalities on general star-like Lip 1 domains. It also explores the case of cuspidal Lip alpha, 0 < alpha < 1 graph domains.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Marco Vogel
Summary: Study on the strong coupling asymptotics of operator Q alpha omega, proving that for large alpha, the behavior of its eigenvalues depends on specific parameters.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Kin Ming Hui, Kai-Seng Chou
Summary: This passage discusses the relationship between nonnegative solutions of the heat equation in a bounded cylindrical domain and their integral representation in terms of a trace triple.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alberto Lastra, Pascal Remy
Summary: In this article, we construct explicit meromorphic solutions of first-order and higher-order linear q-difference equations in the complex domain. We describe the location of all the zeros and poles of these solutions. The study includes both the homogeneous and inhomogeneous cases, with detailed explanations and examples.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Seyf Eddine Ghenimi, Abdelmouhcene Sengouga
Summary: This paper studies small vibrations of a string with a time-varying length ⠂(t) at a speed slower than the speed of vibration propagation. We establish lower and upper bounds for the energy of the string when a dash-pot with a constant damping factor eta is placed at the moving boundary. The estimates explicitly depend on ⠂(t), eta, and a function phi that satisfies the functional equation phi(t + ⠂(t)) - phi(t - ⠂(t)) = 2. (c) 2023 Elsevier Inc. All rights reserved.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
