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
Nguyen Thi Van Anh, Tran Dinh Ke, Do Lan
Summary: We study a class of final value problems governed by semilinear anomalous diffusion equations, where the nonlinearity can take values in Hilbert scales with negative orders. By establishing estimates in Hilbert scales for resolvent operators in connection with nonlinearity function, we prove the solvability and Holder regularity results, which are applicable to some specific problems modeling subdiffusion phenomena.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Yan Zhao, Li Xie
Summary: This paper investigates a two-dimensional parabolic-elliptic system in crime activities, finding the existence of global classical solutions and considering the qualitative behaviors of solutions in large time scales.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Yun-Zhang Li, Ming Yang
Summary: This paper discusses Gabor analysis on locally compact abelian groups and investigates rationallly sampled Gabor frames on L2(R+, d mu) and their properties.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Laura Angeloni, Danilo Costarelli
Summary: This paper introduces and studies a family of exponential-type polynomials, and analyzes their uniform and L-p convergence in suitable function spaces. Estimates are achieved using an exponentially weighted version of the p-norm in the L-p-case. The paper also proves a Voronovskaja type formula to determine the exact order of pointwise approximation for continuous functions with second derivative at some points. Additionally, quantitative estimates for the order of approximation in both the continuous and L-p-cases are established based on the modulus of continuity and K-functionals, with a crucial role played by the Hardy-Littlewood maximal function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Jiguang Bao, Shuai Qi
Summary: This paper studies the non-local diffusion problem with non-local Neumann boundary condition. Integration by parts formulas similar to the Laplacian are established, and the existence, uniqueness, and maximum principle of the solution are proved. The properties of the Neumann condition for one equation and for a family of equations are also investigated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Michal Johanis, Vaclav Krystof, Ludek Zajicek
Summary: Our paper complements a recent article by D. Azagra and C. Mudarra (2021, [2]). We demonstrate how previous results on semiconvex functions with modulus omega can easily lead to extension theorems for C1,omega-smooth functions on super-reflexive Banach spaces, which are variations of Azagra and Mudarra's theorems. We also present some new interesting consequences that were not mentioned in their article, particularly extensions of C1,omega-smooth functions from open quasiconvex sets. Our paper contributes further by presenting our version of their extension theorem for C1,+ B-smooth functions (i.e., functions with uniformly continuous derivative on each bounded set) on Hilbert spaces, as well as new extension results for C1,+ and C1,+ loc-smooth functions (i.e., functions with uniformly and locally uniformly continuous derivative) on arbitrary super-reflexive Banach spaces. Some of our proofs are inspired by the ideas of Azagra and Mudarra's article, but are formally independent of their work.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Richard Nutt, Roland Schnaubelt
Summary: This study investigates the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. The results demonstrate the existence of solutions for small data, which decay exponentially to 0. The improvement in results is achieved by introducing a new trace estimate, an observability-type estimate, and a detailed regularity analysis.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Claudio A. Dimarco
Summary: Zygmund functions are a type of functions that fall between Lipschitz and Holder functions. Their second order divided differences are uniformly bounded. We extend the well-known result about Lipschitz functions to the Zygmund class.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
