Article
Mathematics
Emerson Abreu, Diego Felix, Everaldo Medeiros
Summary: This paper investigates the existence, nonexistence, and multiplicity of solutions for a class of indefinite quasilinear elliptic problems in the upper half-space with weights in anisotropic Lebesgue spaces. The basic tool utilized is a Hardy type inequality established in the paper, enabling the establishment of Sobolev embeddings into Lebesgue spaces with weights in anisotropic Lebesgue spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Ming Tang, Liuqiang Zhong, Yingying Xie
Summary: In this paper, we propose and analyze a modified weak Galerkin (MWG) finite element method for H(curl)-elliptic problem. We introduce a new discrete weak curl operator and the MWG finite element space. The modified weak Galerkin method eliminates the need for penalty parameter compared to traditional DG methods. We prove an optimal error estimate in energy norm and validate the theoretical results with numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics
Amrita Ghosh, Tuhin Ghosh
Summary: This article studies the unique continuation of a perturbed anisotropic fourth-order elliptic operator in elastic beam theory, focusing on the principal and inverse problem. The analysis includes discussions on the three-ball inequality, stability estimate, strong unique continuation principle, and the inverse boundary value problem of recovering material coefficients. (c) 2023 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Tuan Nguyen Huy, Luu Vu Cam Hoan, Yong Zhou, Tran Ngoc Thach
Summary: This study investigates a Cauchy problem for the stochastic elliptic equation driven by Wiener noise, showing it is not well-posed through a simple illustrative example. To regularize the unstable solution, a regularization method called Fourier truncated expansion method is applied, with further investigation into the convergence rate of the regularized solution.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Xiaochun Sun, Huandi Liu
Summary: This work demonstrates the uniqueness of the weak solution to the fractional anisotropic Navier-Stokes system with only horizontal dissipation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Astronomy & Astrophysics
P-F Leget, P. Astier, N. Regnault, M. Jarvis, P. Antilogus, A. Roodman, D. Rubin, C. Saunders
Summary: By utilizing Gaussian process interpolation with a von Karman kernel, we were able to significantly reduce the covariances of astrometric residuals for nearby sources and halve the rms residuals. This approach also enabled us to detect small static astrometric residuals caused by the Hyper Suprime-Cam sensors, with implications for galaxy shape measurements in cosmic shear analyses at the Rubin Observatory Legacy Survey of Space and Time.
ASTRONOMY & ASTROPHYSICS
(2021)
Article
Mathematics, Applied
Kaifang Liu, Peng Zhu
Summary: This paper presents an error analysis of a weak Galerkin method for second-order elliptic equations with minimal regularity requirements. It introduces a new error equation and optimal a priori error estimates, and verifies the theoretical results through numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Junping Wang, Xiaoshen Wang, Xiu Ye, Shangyou Zhang, Peng Zhu
Summary: This article extends the weak Galerkin (WG) approximation for modeling partial differential equations from constant coefficients to variable coefficients and achieves superconvergence. The superconvergence in this case is two-order higher than the optimal-order error estimates in the usual energy and L2 norms. The extension from constant to variable coefficients for the modeling equations is highly complex, and the technical analysis is based on the use of a sequence of projections and decompositions. Numerical results are presented to confirm the superconvergence theory for second-order elliptic problems with variable coefficients.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Shaban H. Kutaiba, Vladimir B. Vasilyev
Summary: The study focuses on a boundary value problem in Sobolev-Slobodetskii spaces with an integral condition, excluding a ray from the origin on a plane. By utilizing an auxiliary problem outside a convex cone and the concept of wave factorization, a general solution is constructed and the transition to the limit boundary value problem is considered. It is demonstrated that the limit boundary value problem can only be solvable if the boundary function satisfies a specific singular functional equation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Chemistry, Multidisciplinary
Yingchun Long, Qiuhua Wu, Chao Jiang, Guolin Zhang, Fuxin Liang
Summary: This study developed an innovative strategy to achieve controlled asymmetric surface partitioned growth on various particles through selective adsorption and growth based on wettability control. Anisotropic Janus particles with multitentacle structure were successfully obtained by integrating emulsion droplets and seed templates.
Article
Mathematics
Astamur Bagapsh, Alexandre Soldatov
Summary: This paper focuses on explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk. It also describes an iterative method for solving this problem for systems with respect to two unknown functions, and an integral representation of the Poisson type obtained through this method.
Article
Physics, Particles & Fields
Hendrik Roch, Nicolas Borghini
Summary: The fluctuations of anisotropic transverse flow due to the finite number of scatterings in a two-dimensional system of massless particles were investigated. Using initial geometries from a Monte Carlo Glauber model, the study showed how flow coefficients fluctuate around their mean value at the corresponding eccentricity for different values of the scattering cross section. Additionally, the evolution of the distributions of the second and third event planes of anisotropic flow about the corresponding participant plane in the initial geometry was demonstrated as a function of the mean number of scatterings in the system.
EUROPEAN PHYSICAL JOURNAL C
(2021)
Article
Engineering, Civil
Chao Zhou, Rui Chen
Summary: The study investigates the influence of anisotropy effects on water retention curve (WRC) of unsaturated soils based on two-dimensional analysis of soil pores. It is found that anisotropic specimen with elongated pores has higher water retention ability compared to isotropic specimen with round pores. A new WRC model is proposed and successfully verified through simulations, demonstrating its capability in capturing the influence of anisotropy on WRC.
JOURNAL OF HYDROLOGY
(2021)
Article
Mathematics, Applied
Saqib Hussain, Xiaoshen Wang, Ahmed Al-Taweel
Summary: This article introduces a modified weak Galerkin finite element method for a second order elliptic problem with mixed boundary conditions, aiming to reduce degrees of freedom and establish optimal convergence orders. Numerical examples are provided to verify the theoretical estimates, which are published by Elsevier B.V.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Abdolrahman Razani
Summary: This paper considers an anisotropic equation on the Heisenberg group Hn and proves the existence of entire weak solutions using variational methods.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Ravi P. Agarwal, Ahmad M. A. Alghamdi, Sadek Gala, Maria Alessandra Ragusa
Summary: This research paper deals with the blow-up criterion of local smooth solution to the 3D Hall-magnetohydrodynamics equations in Besov spaces.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics
F. Deringoz, V. S. Guliyev, M. N. Omarova, M. A. Ragusa
Summary: This paper investigates the boundedness of Calderon-Zygmund operators and their commutators in generalized weighted Orlicz-Morrey spaces, as well as the boundedness in the vector-valued setting.
BULLETIN OF MATHEMATICAL SCIENCES
(2023)
Article
Mathematics, Applied
Maria Alessandra Ragusa, Abdolrahman Razani, Farzaneh Safari
Summary: In this study, a variational principle is used to examine a Muckenhoupt weighted p-Laplacian equation on the Heisenberg groups. The existence of at least one positive radial solution to the problem under the Dirichlet boundary condition in the first order Heisenberg-Sobolev spaces is proven.
Article
Mathematics
Ravi P. Agarwal, Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa
Summary: In this paper, we establish a regularity criterion for micropolar fluid flows by introducing the one component of the velocity in critical Morrey-Campanato space. Specifically, we prove that if Z0 T 24 9 symbolscript < infinity, where 0 < r < M2, 3 10, r, then the weak solution (u, w) is regular.
MATHEMATICAL MODELLING AND ANALYSIS
(2023)
Article
Mathematics, Applied
Munirah Alotaibi, Mohamed Jleli, Maria Alessandra Ragusa, Bessem Samet
Summary: This paper investigates an initial value problem for a nonlinear time-fractional Schrodinger equation with a singular logarithmic potential term. The problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Sufficient criteria for the absence of global weak solutions are obtained using the test function method with a judicious choice of the test function.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics
Long Le Dinh, Duc Phuong Nguyen, Maria Alessandra Ragusa
Summary: This paper aims to retrieve the initial value for a non-local fractional Sobolev-Galpern problem. The Fourier truncation method is applied to construct the regularized solution, and the convergence between the solution and the regularized solution is estimated. Additionally, a numerical example is proposed to assess the efficiency of the theory.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics, Applied
Hamza Boujemaa, Badr Oulgiht, Maria Alessandra Ragusa
Summary: This paper introduces a new class of fractional Orlicz-Sobolev space with variable-order. The basic properties of this space are given and some compactness results are proved. Then, using techniques of calculus of variations combined with the theory of Musielak functions, the existence of a nonnegative weak solution for a singular elliptic type problem in a fractional variable-order Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions is proved. (c) 2023 Elsevier Inc. All rights reserved.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Nabil Chems Eddine, Phuong Duc Nguyen, Maria Alessandra Ragusa
Summary: In this article, the existence and infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters are obtained by combining the variational method and the concentration-compactness principle.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
V. S. Guliyev, Meriban N. N. Omarova, Maria Alessandra Ragusa
Summary: In this article, the continuity of commutators [b, T] of Calderón-Zygmund operators with BMO functions in generalized Orlicz-Morrey spaces M-F, M-f(R-n) is demonstrated. Necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T and their commutators [b, T] on generalized Orlicz-Morrey spaces are provided.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Mathematics
Ravi P. Agarwal, Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa
Summary: In this article, the regularity criteria for weak solutions of the Boussinesq equations are studied, focusing on the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. The results highlight the dominant role of the velocity field in the regularity theory of the Boussinesq equations.
DEMONSTRATIO MATHEMATICA
(2023)
Article
Mathematics, Applied
Ines Ben Omrane, Mourad Ben Slimane, Sadek Gala, Maria Alessandra Ragusa
Summary: This paper investigates the regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. It is proven that the weak solution is regular on (0, T] if the pressure satisfies either the norm IIπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=2 and 32<β<∞ or IIVπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=3 and 1<β<∞ is sufficiently small.
Article
Mathematics, Applied
Ben Omrane Ines, Gala Sadek, Ragusa Maria Alessandra
Summary: This paper studies the logarithmically improved regularity criterion of the 3D Boussinesq equations using the middle eigenvalue of the strain tensor in Besov spaces with negative indices. It shows that a weak solution becomes regular on (0, T] if the given inequality holds for some 0 < δ < 1. This result improves upon the previous works by Neustupa-Penel and Miller.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2023)
Article
Mathematics, Applied
Hamdy M. Ahmed, A. M. Sayed Ahmed, Maria Alessandra Ragusa
Summary: By using Monch fixed point theorem, fractional calculus, and stochastic analysis, this paper establishes sufficient conditions for the existence of solutions to non-instantaneous impulsive Hilfer-Katugampola fractional differential equations of order 1/2 < alpha < 1 and parameter 0 <= beta <= 1 with fractional Brownian motion (fBm), Poisson jumps, and nonlocal conditions. An example is provided to illustrate the obtained results.
TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Aidyn Kassymov, Maria Alessandra Ragusa, Michael Ruzhansky, Durvudkhan Suragan
Summary: In this study, we establish the Adams type Stein-Weiss inequality on general homogeneous groups and demonstrate its applications on Morrey spaces. These results are not only new for general homogeneous groups, but also for the Euclidean space.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Mohamed Jleli, Maria Alessandra Ragusa, Bessem Samet
Summary: This paper studies differential inequalities of a specific form and establishes necessary conditions for the existence of nontrivial weak solutions. The proof is based on the nonlinear capacity method and a result by Bianchi and Setti (2018).
ADVANCES IN DIFFERENTIAL EQUATIONS
(2023)
