Article
Mechanics
Rafael Granero-Belinchon, Stefano Scrobogna
Summary: The paper examines the motion of viscous water waves and introduces a new asymptotic model. Global well-posedness in Sobolev spaces is established, as well as the global well-posedness and decay of a fourth order partial differential equation modeling bidirectional water waves with viscosity moving in deep water with or without surface tension effects.
Article
Mathematics, Applied
Yunfei Su, Zilai Li, Lei Yao
Summary: This paper studies the global existence of weak solutions to a reduced gravity two-and-a-half layer model in oceanic fluid dynamics on a two-dimensional torus. Using the Faedo-Galerkin method and weak convergence method, global weak solutions renormalized in the velocity variable are constructed. It is proved that the renormalized solutions are weak solutions satisfying the basic energy inequality and Bresch-Desjardins entropy inequality, but not the Mellet-Vasseur type inequality. The research results are important for understanding oceanic fluid dynamics.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Rudong Zheng, Zhaoyang Yin, Boling Guo
Summary: In this study, global weak solutions to the Novikov equation are investigated using the vanishing viscosity method. It is proven that global weak solutions can be obtained as weak limits of viscous approximations for a specific class of initial data. The proof relies on a higher integrability estimate in space and time, as well as the method of renormalization. Additionally, the interaction of peakons and antipeakons is analyzed, and it is shown that wave breaking leads to energy concentration. Conservative solutions and dissipative solutions are obtained by different continuations beyond the wave breaking.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Automation & Control Systems
George Jiroveanu, Rene K. K. Boel
Summary: In this article, we examine the distributed analysis of a plant using local Petri net models that interact through shared transitions. Each component has a local agent that performs calculations and exchanges information with its neighbors for plant monitoring. We relax the requirement that the interaction graph between components is a tree and investigate the conditions under which the local consistency of estimates implies their global consistency. Furthermore, we demonstrate that incorporating additional information related to the execution time intervals of shared transitions in the exchanged information between agents results in globally consistent estimates equivalent to those derived in a CR.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Mathematics
Lin Ma, Boling Guo, Jie Shao
Summary: This study proves the existence of global weak solutions with finite energy to two-fluid systems with magnetic field, which are suitable for corresponding two-fluid systems. The proof method is inspired by previous works and allows for more explicit proof without unnecessary conditions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Quansen Jiu, Jitao Liu, Dongjuan Niu
Summary: This paper proves the global existence of weak solutions to the incompressible axisymmetric Euler equations without swirl under specific conditions on the initial vorticity, without the requirement of finite initial energy. Finite initial velocity belonging to certain function spaces is considered. The key part of the proof involves establishing new estimates for velocity fields.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mathematics, Applied
Hantaek Bae, Woojae Lee, Jaeyong Shin
Summary: This paper analyzes a nonlinear model of the viscous water-waves equation proposed in Dias et al. (2008). The linear model in Dias et al. (2008) is first studied, and then a new model that approximates the nonlinear model is derived. The existence of a unique global-in-time solution and its decay rates to this new system with small initial data in energy spaces are finally demonstrated.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Daisuke Hirata
Summary: In this note, we consider a Schrodinger evolution equation with a power nonlinearity and a viscous damping term. We demonstrate the global existence of classical solutions with finite mass for the Cauchy problem. Furthermore, our proof is also applicable for a nonlinear complex Ginzburg-Landau equation.
JOURNAL OF EVOLUTION EQUATIONS
(2022)
Article
Mathematics, Applied
Jakub Wiktor Both, Iuliu Sorin Pop, Ivan Yotov
Summary: This study focuses on unsaturated poroelasticity in variably saturated porous media, using a model similar to Biot's and Richards' equations. The existence of weak solutions is established through numerical approximation and finite element/finite volume discretization, with solvability of the original problem demonstrated using a combination of Rothe and Galerkin methods. The final existence result is dependent on non-degeneracy conditions and natural continuity properties for the constitutive relations, which are shown to be reasonable for geotechnical applications.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2021)
Article
Mathematics
Duong Trong Luyen, Ha Tien Ngoan, Phung Thi Kim Yen
Summary: In this paper, we investigate the existence and non-existence of weak solutions for the semilinear bi-Delta(gamma)-Laplace equation. By considering the bounded domain with smooth boundary and imposing specific boundary conditions, we solve the equation.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Mechanics
Nils T. Basse
Summary: The study extends a procedure outlined in Basse's work to investigate the global scaling of streamwise velocity fluctuations and identifies a transition at a friction Reynolds number of order 10000. The position and amplitude of the global peak are characterized and the impact of including an additional wake term is analyzed.
Article
Mathematics
Duong Trong Luyen, Ha Tien Ngoan, Phung Thi Kim Yen
Summary: This paper investigates the existence and non-existence of weak solutions for the semilinear bi-Delta(gamma)-Laplace equation, involving a bounded domain with smooth boundary in R-N, a Caratheodory function, and the subelliptic operator Delta(gamma).
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Astronomy & Astrophysics
Ashadul Halder, Shashank Shekhar Pandey, A. S. Majumdar
Summary: We examine the global 21-cm brightness temperature in the context of viscous dark energy models and study the effects of Hawking radiation, decay and annihilation of particle dark matter, and baryon-dark matter scattering on the temperature. Our analysis provides bounds on the parameters of the viscous dark energy model that can account for the observed excess in the EDGES experiment. Additionally, our study yields modified constraints on the dark matter mass and scattering cross-section compared to the conventional ACDM model.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Genilson S. Lima, Pedro S. Peixoto
Summary: The increasing number of cores in modern supercomputers has led to the search for scalable methods for modeling global problems in geophysical fluid dynamics. Grid-point schemes with quasi-uniform spherical grids and explicit time integration are one of the options for dynamical core developments. However, they may have low accuracy or errors induced by the grid. In this study, a method for solving the shallow water equations on a C-staggered global reduced grid is proposed, which shows adequate accuracy at competitive computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Eduard Feireisl, Antonin Novotny
Summary: This study extends the weak-strong uniqueness principle to general models of compressible viscous fluids near/on the vacuum, focusing on the physically relevant case of positive density with polynomial decay at infinity.
Article
Construction & Building Technology
C. Ramirez-Balas, E. D. Fernandez-Nieto, G. Narbona-Reina, J. J. Sendra, R. Suarez
ENERGY AND BUILDINGS
(2015)
Article
Mathematics, Applied
F. Bouchut, E. D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2015)
Article
Mathematics, Applied
Enrique D. Fernandez-Nieto, Tomas Morales de Luna, Gladys Narbona-Reina, Jean de Dieu Zabsonre
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2017)
Article
Mechanics
Francois Bouchut, Enrique D. Fernandez-Nieto, Anne Mangeney, Gladys Narbona-Reina
JOURNAL OF FLUID MECHANICS
(2016)
Article
Mechanics
E. D. Fernandez-Nieto, J. Garres-Diaz, A. Mangeney, G. Narbona-Reina
JOURNAL OF FLUID MECHANICS
(2016)
Article
Computer Science, Interdisciplinary Applications
Luca Bonaventura, Enrique D. Fernandez-Nieto, Jose Garres-Diaz, Gladys Narbona-Reina
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Computer Science, Interdisciplinary Applications
E. D. Fernandez-Nieto, J. Garres-Diaz, A. Mangeney, G. Narbona-Reina
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Energy & Fuels
Cristina Ramirez-Balas, Enrique Fernandez-Nieto, Gladys Narbona-Reina, Juan Jose Sendra, Rafael Suarez
Article
Mathematics, Applied
Manuel Jesus Castro Diaz, Enrique Domingo Fernandez-Nieto, Tomas Morales de Luna, Gladys Narbona-Reina, Carlos Pares
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2013)
Article
Computer Science, Interdisciplinary Applications
M. J. Castro Diaz, E. D. Fernandez-Nieto, G. Narbona-Reina, M. de la Asuncion
JOURNAL OF COMPUTATIONAL PHYSICS
(2014)
Article
Computer Science, Interdisciplinary Applications
J. M. Delgado-Sanchez, F. Bouchut, E. D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Computer Science, Interdisciplinary Applications
J. Garres-Diaz, F. Bouchut, E. D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Computer Science, Interdisciplinary Applications
Francois Bouchut, Enrique D. Fernandez-Nieto, El Hadji Kone, Anne Mangeney, Gladys Narbona-Reina
Summary: This study investigates the dilatancy effects in dry granular flows, revealing that initial volume fraction affects the height of deposits but has little impact on the front position and deposit shape. The model predicts increasing dilation of the mass with increasing slopes, indicating the key role of dilatancy in describing granular flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
F. Bouchut, J. M. Delgado-Sanchez, E. D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina
Summary: Depth-averaged models may fail to preserve the physical threshold of motion in certain cases due to the hydrostatic pressure assumption. This paper proposes a correction method that modifies the friction term and introduces a second-order pressure correction based on slow granular flows. Numerical tests demonstrate that the proposed correction effectively addresses the issues in classical depth-averaged models and is consistent with experimental data. However, further improvements are needed to address the limitations of the correction method in the starting and stopping phases of granular avalanches.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
J. Garres-Diaz, E. D. Fernandez-Nieto, G. Narbona-Reina
Summary: This work proposes efficient semi-implicit methods for sediment bedload transport models with gravitational effects under subcritical regimes. Several families of models with gravitational effects are presented and rewritten under a general formulation, allowing the application of the semi-implicit method. In the numerical tests, the focus is on a generalization of the Ashida-Michiue model, which includes the gradient of both the bedload and the fluid surface. Analytical steady state solutions (both lake at rest and non-vanishing velocity) are deduced and approximated using the proposed scheme. In all the presented tests, the computational efforts are notably reduced without compromising the accuracy of the results.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
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)
