Article
Polymer Science
Changhao Li, Jianfeng Li, Yuliang Yang
Summary: This work derives a more accurate reaction-diffusion equation for an A/B binary system by summing over microscopic trajectories and introduces the DRD diagram method. It is found that there are coupling terms between diffusion and reaction when there is intermolecular interaction, manifesting on the mesoscopic scale. This method can also be applied to describe chemical reactions in polymeric systems.
Article
Mathematics, Interdisciplinary Applications
Syed Ahmed Pasha, Yasir Nawaz, Muhammad Shoaib Arif
Summary: The nonstandard finite difference method is a superior approach to numerically solve nonlinear differential equations, as it overcomes the instability and bias of standard finite difference methods. A recent issue with nonstandard finite difference schemes is the lack of first-order temporal accuracy or consistency for important models like diffusion and reaction-diffusion systems. This paper proposes an alternative nonstandard finite difference scheme that guarantees first-order accuracy in time and second-order accuracy in space while preserving solution positivity. Stability and consistency analyses are presented, along with comparisons to existing schemes that confirm the superiority of the proposed approach.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Shujuan Lu, Tao Xu, Zhaosheng Feng
Summary: In this study, a second-order finite difference scheme is proposed for analyzing a class of space-time variable-order fractional diffusion equation. The scheme is demonstrated to be unconditionally stable and convergent with a convergence order of O(tau(2) + h(2)) under certain conditions, as validated by numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Qi Wang
Summary: In this paper, the dynamics of a reaction-diffusion-advection system modeling populations in a polluted river are investigated. The stability of steady states is specifically studied, providing sufficient conditions for population persistence or extinction. Additionally, the dependence of the stability of the toxicant-only steady state and the population-toxicant coexistence steady state on the model parameters is given.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Jin Zhang, Xiaowei Liu
Summary: The implicit Euler method and the streamline upwind Petrov Galerkin (SUPG) method were used to solve the evolutionary convection-diffusion-reaction equation, obtaining uniform stability with respect to the temporal and spatial discretization parameters. A new projection was introduced for stability analysis instead of the common idea of material derivative, allowing flexibility in the relation between time step and space step. This analysis can also handle time-dependent convection and reaction coefficients.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Sihui Zhang, Xiangyu Shi, Dongyang Shi
Summary: The nonconforming modified Quasi-Wilson finite element method is used to investigate the unconditional superconvergence behavior of the convection-diffusion-reaction equation. The energy stabilities of the discrete solutions for the proposed schemes are demonstrated through mathematical induction. Superconvergence properties for the schemes are derived by the interpolation post-processing technique and validated through numerical experiments.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Yu Liu, Guanggan Chen, Shuyong Li
Summary: In this paper, the nonlinear orbital stability of the traveling wave solution for deterministic and stochastic delayed reaction-diffusion equation is established. The exponential stability of the traveling wave solution for the deterministic equation is obtained by employing a deterministic phase shift and establishing a delayed-integral inequality. It is verified that the traveling wave solution of the deterministic equation retains the nonlinear orbital stability when the noise intensity is sufficiently small and the initial value sufficiently closes the traveling wave by applying a stochastic phase shift and time transformation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
Summary: This study investigates a general system consisting of several ordinary differential equations and a reaction-diffusion equation in a bounded domain. The main finding is the instability of all regular patterns, suggesting that stable stationary solutions in models with non-diffusive components must be far-from-equilibrium and exhibit singularities.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Multidisciplinary Sciences
Endre Kovacs, Adam Nagy, Mahmoud Saleh
Summary: Introduces a new explicit numerical method for the diffusion or heat equation, which discretizes the space variables and analytically solves the time derivatives using a combination of constant-neighbor and linear-neighbor approximations, providing unconditional stability and third-order convergence.
ADVANCED THEORY AND SIMULATIONS
(2022)
Article
Mathematics, Applied
Isaac P. Santos, Sandra M. C. Malta, Andrea M. P. Valli, Lucia Catabriga, Regina C. Almeida
Summary: This study introduces a new variant of the nonlinear multiscale Dynamic Diffusion (DD) method, which provides additional stability through a dynamic nonlinear operator acting in all scales. The paper proves the existence of discrete solutions, stability, and a priori error estimates, and theoretically shows that the new DD method has a convergence rate of O(h(1/2)) in the energy norm. Numerical experiments also confirm optimal convergence rates in various norms.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Antonin Slavik
Summary: The study focuses on reaction-diffusion equations on graphs, exploring the conditions for the existence of spatially heterogeneous stationary states and the construction of Lyapunov functions. The results indicate an easy-to-use method applicable in cases where the non-diffusive Lyapunov function is a sum of univariate functions with nondecreasing derivatives.
Article
Mathematics, Applied
Zi-Hang She, Hai-Dong Qu, Xuan Liu
Summary: This paper investigates and analyzes the Crank-Nicolson temporal discretization method with certain spatial difference schemes for one- and two-dimensional two-sided space-fractional diffusion equations with variable diffusion coefficients. The stability and convergence of the resulting discretization linear systems for equations with variable diffusion coefficients are proven by a new technique, showing unconditional stability and convergence with an error of O(tau(2)+h(l)) (l >= 1). Additionally, numerical examples are provided to illustrate the theoretical analyses.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Physics, Mathematical
Wenjie Hu, Quanxin Zhu
Summary: This paper focuses on the existence of a random attractor for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) under a Dirichlet boundary condition. By adopting the random dynamical system theory together with the stochastic inequality technique, the authors first provide a uniform estimate of the solution and then prove the asymptotic compactness of the random dynamic system generated by the SNDRDE. The existence of a random attractor is subsequently obtained.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Deeksha Singh, Rajesh K. Pandey, Sarita Kumari
Summary: In this work, a high-order numerical scheme is proposed and analyzed to solve the non-linear time fractional reaction-diffusion equation. The scheme consists of a time-stepping cubic approximation for the time fractional derivative and a compact finite difference scheme to approximate the spatial derivative. The proposed scheme is proven to be unique solvable, stable, and convergent.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mathematics
Hirokazu Ninomiya, Hiroko Yamamoto
Summary: This paper introduces a reaction-diffusion system whose solutions approximate those of a semilinear wave equation under certain assumptions of a reaction term, with the proof based on the energy method.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)