Article
Mathematics, Applied
N. Valliammal, K. Jothimani, M. Johnson, Sumati Kumari Panda, V. Vijayakumar
Summary: This article primarily focuses on studying the existence and approximate controllability of impulsive neutral functional hemivariational inequalities. The existence of mild solutions and approximate controllability results are formulated and proven using the theory of semigroup of operators, a fixed point theorem of multivalued maps, and properties of generalized Clarke subdifferential. Finally, some examples are provided to illustrate the applicability of the main results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Operations Research & Management Science
S. Vivek, V. Vijayakumar
Summary: In this paper, we investigate the approximate controllability of a neutral hemivariational inequality with impulses. We first derive the mild solution for the given system and then utilize semigroup theory, fixed point theorem of multivalued map, and properties of generalized Clarke's subdifferentials to prove the existence and approximate controllability results. Finally, we provide an example to illustrate our theory.
Article
Mathematics, Applied
Jiangfeng Han, Changpin Li, Shengda Zeng
Summary: This paper studies a generalized fractional hemivariational inequality in infinite-dimensional spaces and delivers an existence result using the temporally semi-discrete scheme and the surjectivity result for multivalued pseudomonotone operator. As an illustrative application, a frictional contact model describing the quasi-static contact between a viscoelastic body and a solid foundation is proposed. The weak solvability of the mechanical system is obtained by using the abstract mathematical result presented in this paper.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Mircea Sofonea
Summary: This paper discusses a variational-hemivariational inequality in a real Hilbert space with two parameters. It proves that the inequality is governed by a maximal monotone operator and deduces various existence, uniqueness, and equivalence results. These results lay the foundation for studying different classes of inequalities and are used to solve elliptic and history-dependent variational-hemivariational inequalities. The paper also introduces iterative methods and convergence results.
Article
Mathematics, Applied
Emilio Vilches, Shengda Zeng
Summary: This paper proposes a new methodology for studying evolutionary variational-hemivariational inequalities based on the theory of evolution equations and maximal monotone operators. The proposed approach explores well-posedness for problems involving history-dependent operators and periodic/antiperiodic boundary conditions, and is illustrated through applications to fractional evolution inclusions and dynamic semipermeability problems.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2021)
Article
Mathematics, Applied
Krzysztof Bartosz, Pawel Szafraniec, Jing Zhao
Summary: In this paper, we investigate a first-order evolution inclusion involving a multivalued term generated by a Clarke subdifferential. Using the Rothe scheme, we construct a double step time-semidiscrete approximation for this problem. By studying the sequence of solutions of the semidiscrete approximate problems, we establish weak convergence to a limit element, which is a solution of the original problem.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Yi-bin Xiao, Mircea Sofonea
Summary: The study focuses on an elliptic variational-hemivariational inequality with constraints, providing unique solutions and proving convergence under certain operator conditions. The results are applied in various scenarios, including a variational-hemivariational inequality with unilateral constraints in Contact Mechanics. The abstract convergence result is illustrated and provides corresponding mechanical interpretations.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Ouayl Chadli, Jen-Chih Yao
Summary: This paper tackles a nonconvex constrained variational-hemivariational inequality problem for a star-shaped set, demonstrating the existence of solutions using equilibrium problem theory and a penalization method. An application to a nonconvex constrained semipermeability model for the stationary heat conduction problem is also provided. The results are novel and substantially advance the recent literature.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Mircea Sofonea, Yi-bin Xiao, Sheng-da Zeng
Summary: In this paper, a history-dependent variational-hemivariational inequality with unilateral constraints in a reflexive Banach space is considered. A generalized penalty method associated to the inequality is introduced and studied. The unique solvability of penalty problems and the convergence of solutions sequence to the original problem are proved, extending previous results.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics, Applied
Calogero Vetro
Summary: We studied a nonlinear p(x)-Kirchhoff type problem with Dirichlet boundary condition, where the reaction term also depends on the gradient. By using a topological approach based on the Galerkin method, we discussed the existence of two types of solutions: strong generalized solution and weak solution. By strengthening the bound on the Kirchhoff type term, we established the existence of weak solutions using the theory of operators of monotone type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Yongjian Liu, Stanislaw Migorski, Van Thien Nguyen, Shengda Zeng
Summary: This paper studies a mathematical model of a nonlinear static frictional contact problem in elasticity, including the weak formulation of the contact model, the solvability of the contact problem, and the convergence of solutions under perturbations in the elasticity operator, body forces, and surface tractions using H-convergence of nonlinear elasticity tensors.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Operations Research & Management Science
Jing Li, Maojun Bin
Summary: This paper focuses on control systems described under certain conditions, and investigates the properties of the control constraints as well as the relaxation properties among the solution sets.
Article
Engineering, Multidisciplinary
Yong-Ki Ma, C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar
Summary: This paper discusses the approximate controllability of hemivariational inequalities of the Sobolev-type Hilfer fractional neutral stochastic evolution system. Firstly, by using fixed point theorems, fractional calculus, Hilfer fractional derivatives, multivalued maps, and stochastic analysis, we demonstrate the existence of mild solutions for these stochastic fractional evolution systems. Then, we introduce necessary conditions that ensure the approximate controllability of stochastic fractional systems. Finally, we define our primary outcomes using an example.
AIN SHAMS ENGINEERING JOURNAL
(2023)
Article
Operations Research & Management Science
Ouayl Chadli, Gabor Kassay, Asma Saidi
Summary: By leveraging recent developments in equilibrium problems theory, the study focuses on the existence of antiperiodic solutions for a first order hemivariational inequality problem associated with time dependent pseudomonotone and quasimonotone operators. The new results presented in the study introduce an efficient approach for addressing hemivariational inequality problems.
OPTIMIZATION LETTERS
(2021)
Article
Mathematics, Applied
Jinxia Cen, Chao Min, Mircea Sofonea, Shengda Zeng
Summary: This article investigates a hemivariational inequality of elliptic type in a reflexive Banach space, proving its solvability and the compactness of its solution set. The author uses a surjectivity theorem for multivalued mappings to study the sum of a maximal monotone operator and a bounded pseudomonotone operator. The concepts of strongly and weakly well-posedness for the hemivariational inequality are introduced, along with two characterizations for strongly well-posedness under different assumptions on the data. The article also provides sufficient conditions for weakly and strongly well-posedness of the hemivariational inequality, and considers two perturbations for which convergence results in the sense of Kuratowski are obtained.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Krzysztof Bartosz, Piotr Kalita, Stanislaw Migorski, Anna Ochal, Mircea Sofonea
APPLIED MATHEMATICS AND OPTIMIZATION
(2016)
Article
Mathematics, Applied
Leszek Gasinski, Anna Ochal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2015)
Article
Mathematics, Applied
Stanislaw Migorski, Anna Ochal, Mircea Sofonea
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2015)
Article
Mathematics, Applied
Leszek Gasinski, Anna Ochal, Meir Shillor
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
(2015)
Article
Engineering, Multidisciplinary
Stanislaw Migorski, Anna Ochal, Mircea Sofonea
JOURNAL OF ELASTICITY
(2017)
Article
Mathematics, Applied
Leszek Gasinski, Anna Ochal, Meir Shillor
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2016)
Article
Mathematics, Applied
Leszek Gasinski, Stanislaw Migorski, Anna Ochal, Zijia Peng
APPLIED MATHEMATICS AND COMPUTATION
(2018)
Article
Mathematics, Applied
Leszek Gasinski, Stanislaw Migorski, Anna Ochal
APPLICABLE ANALYSIS
(2015)
Article
Mathematics, Applied
Michal Jureczka, Anna Ochal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Xiaoliang Cheng, Qichang Xiao, Stanislaw Migorski, Anna Ochal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Operations Research & Management Science
Leszek Gasinski, Zhenhai Liu, Stanislaw Migorski, Anna Ochal, Zijia Peng
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2015)
Article
Mathematics, Applied
Stanislaw Migorski, Anna Ochal, Meir Shillor, Mircea Sofonea
APPLICABLE ANALYSIS
(2018)
Article
Mathematics, Applied
Anna Ochal, Michal Jureczka
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2018)
Article
Mechanics
Leszek Gasinski, Anna Ochal
JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS
(2015)
Proceedings Paper
Operations Research & Management Science
Stanislaw Migorski, Anna Ochal, Mircea Sofonea
OPTIMIZATION AND CONTROL TECHNIQUES AND APPLICATIONS
(2014)
Article
Mathematics, Applied
Torsten Lindstrom
Summary: This paper aims to analyze the mechanism for the interplay of deterministic and stochastic models in contagious diseases. Deterministic models usually predict global stability, while stochastic models exhibit oscillatory patterns. The study found that evolution maximizes the infectiousness of diseases and discussed the relationship between herd immunity concept and vaccination programs.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Dong Deng, Hongxun Wei
Summary: This paper investigates the existence and nonexistence of time-periodic traveling waves for a diffusive influenza model with treatment and seasonality. By utilizing the next generation operator theory and Schauder's fixed point theorem, the conditions for the existence of time-periodic traveling wave solutions are obtained, along with the proof of nonexistence in certain cases and exponential decay for waves with critical speed.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Xuan Ma, Yating Wang
Summary: In this paper, the dynamics of a rarefied gas in a finite channel is studied, specifically focusing on the phenomenon of Couette flow. The authors demonstrate that the unsteady Couette flow for the Boltzmann equation converges to a 1D steady state and derive the exponential time decay rate. The analysis holds for all hard potentials.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Meng Zhao
Summary: In this paper, a reaction-diffusion waterborne pathogen model with free boundary is studied. The existence of a unique global solution is proved, and the longtime behavior is analyzed through a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are obtained, which differs from the previous results by Zhou et al. (2018) stating that the epidemic will spread when the basic reproduction number is larger than 1.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Gulsemay Yigit, Wakil Sarfaraz, Raquel Barreira, Anotida Madzvamuse
Summary: This study presents theoretical considerations and analysis of the effects of circular geometry on the stability of reaction-diffusion systems with linear cross-diffusion on circular domains. The highlights include deriving necessary and sufficient conditions for cross-diffusion driven instability and computing parameter spaces for pattern formation. Finite element simulations are also conducted to support the theoretical findings. The study suggests that linear cross-diffusion coupled with reaction-diffusion theory is a promising mechanism for pattern formation.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Miaoqing Tian, Lili Han, Xiao He, Sining Zheng
Summary: This paper studies the attraction-repulsion chemotaxis system of two-species with two chemical substances. The behavior of solutions is determined by the interactions among diffusion, attraction, repulsion, logistic sources, and nonlinear productions in the system. The paper provides conditions for the global boundedness of solutions.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Michal Borowski, Iwona Chlebicka, Blazej Miasojedow
Summary: This article provides a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff-Havin-Maz'ya type. It characterizes the potentials that are bounded between rearrangement invariant spaces via a one-dimensional inequality of Hardy-type. By controlling very weak solutions to a broad class of quasilinear elliptic PDEs of non-standard growth, the special case of the mentioned potential infers the local regularity properties of solutions in rearrangement invariant spaces for prescribed classes of data.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Young-Pil Choi, Jinwook Jung
Summary: This study investigates the global-in-time well-posedness of the pressureless Euler-alignment system with singular communication weights. A global-in-time bounded solution is constructed using the method of characteristics, and uniqueness is obtained via optimal transport techniques.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Chuangxia Huang, Xiaodan Ding
Summary: In this paper, a diffusive Mackey-Glass model with distinct diapause and developmental delays is proposed based on the diapause effect. Some sufficient conditions for the existence of traveling wave fronts are obtained by constructing appropriate upper and lower solutions and employing inequality techniques. Two numerical examples are provided to demonstrate the reliability and feasibility of the proposed model.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Hongxing Zhao
Summary: This paper investigates the flow of fluid through a thin corrugated domain saturated with porous medium, governed by the Navier-Stokes model. Asymptotic models are derived by comparing the relation between a and the size of the periodic cylinders. The homogenization technique based on the generalized Poincare inequality is used to prove the main results.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Evgenii S. Baranovskii, Roman V. Brizitskii, Zhanna Yu. Saritskaia
Summary: This paper proves the solvability of optimal control problems for both weak and strong solutions of a boundary value problem associated with the nonlinear reaction-diffusion-convection equation with variable coefficients. In the case of strong solutions, the requirements for smoothness of the multiplicative control are reduced. The study of extremal problems is based on the proof of solvability of the corresponding boundary value problems and the qualitative analysis of their solution properties. The paper establishes existence results for weak solutions with large data, the maximum principle, and local existence and uniqueness of a strong solution. Furthermore, an optimal feedback control problem is considered, and sufficient conditions for its solvability in the class of weak solutions are obtained using methods of the theory of topological degree for set-valued perturbations.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Antonia Chinni, Beatrice Di Bella, Petru Jebelean, Calin Serban
Summary: This article focuses on the multiplicity of solutions for differential inclusions involving the p-biharmonic operator, applying a variational approach and relying on non-smooth critical point theory.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhong Tan, Saiguo Xu
Summary: This paper investigates the Rayleigh-Taylor instability of three-dimensional inhomogeneous incompressible Euler equations with damping in a horizontal slab. It is shown that the Euler system with damping is nonlinearly unstable around the given steady state if the steady density profile is non-monotonous along the height. A new variational structure is developed to construct the growing mode solution, and the difficulty in proving the sharp exponential growth rate is overcome by exploiting the structures in linearized Euler equations. Combined with error estimates and a standard bootstrapping argument, the nonlinear instability is established.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Samuele Ricco, Andrea Torricelli
Summary: This paper presents a solution method for the autonomous obstacle problem, finding a necessary condition for the extremality of the unique solution using a primal-dual formulation. The proof is based on classical arguments of Convex Analysis and Calculus of Variations' techniques.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Mathematics, Applied
Shuxin Ge, Rong Yuan, Xiaofeng Zhang
Summary: This paper studies an initial boundary value problem for a nonlocal parabolic equation with a diffusion term and convex-concave nonlinearities. By establishing the Lq-estimate and analyzing its energy, the existence of global solutions is proven and some blow-up conditions are obtained. Using the variational structure of the problem, the Mountain-pass theorem is utilized to demonstrate the existence of nontrivial steady-state solutions. The dynamical behavior of global solutions with relatively compact trajectories in H01 (Ω) is also established, showing uniform convergence to a non-zero steady state after a long time due to the energy functional satisfying the P.S. condition. Finally, an unstable steady states sequence is derived using another minimax theorem.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)