This paper introduces an efficient meshless method for solving 2D nonlinear Volterra integro-differential equations with tempered fractional kernels. It uses a compact radial basis function (RBF)-based partition of unity approach for spatial discretization, transforming the original problem into a semi-discrete system. Hermite-Birkhoff RBF interpolation is employed within partition of unity patches, using both smooth and discontinuous weight functions to construct the global solution. Discontinuous weights yield a sparse global matrix, enhancing computational efficiency. The method also leverages the scaling property of polyharmonic spline kernels for robust local approximations. For time discretization, a convolution quadrature rule with a second-order backward differentiation formula is used. Numerical experiments, including problems without exact solutions, confirm the method's accuracy, robustness, and efficiency.

In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption: { u t = Δ ( D ( u ) ϕ ( v ) ) + ρu ( 1 − u l − 1 ) , ( x , t ) ∈ Ω × ( 0 , ∞ ) , v t = Δ v − vw , ( x , t ) ∈ Ω × ( 0 , ∞ ) , w t = − δw + u , ( x , t ) ∈ Ω × ( 0 , ∞ ) , under the smooth bounded domain Ω ⊂ R 2 with homogeneous Neumann boundary conditions, where the nonlinearities D ( u ) = ( u + 1 ) m with m>0 and the motility function ϕ satisfies the condition: ϕ ∈ C 3 ( ( 0 , ∞ ) ) is positive on [ 0 , ∞ ) . It is proved that the system possesses a unique global classical solution that is uniformly bounded. Moreover, if 0 $ ]]> ρ > 0 , the asymptotic behavior of the solution is discussed.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III

Global large solutions to an initial-boundary value problem of the incompressible ideal MHD equations with velocity damping

Global and singular solution to a nonlocal model of three-dimensional incompressible Navier–Stokes equations

Optimal decay of global strong solutions to nematic liquid crystal flows in the half-space

Antimicrobial resistance (AMR) is one of the highest critical issues causing global health in the 21st century, jeopardizing the chances of efficacy of antibiotics or any other form of antimicrobial agents. Microorganisms like bacteria, viruses, fungi, and parasites develop resistance to drugs that once efficiently cured the infection, making them difficult or even impossible to treat. This current phenomenon adds up to a grave public health problem that increases morbidity and mortality rates and healthcare costs all around the world. The WHO lists AMR among the ten topmost threats to global public health, thereby needing urgent coordinated efforts among governments, healthcare providers, and the public to curtail its spread. There are several actors in the rise of AMR; principally among them are overuse and misuse of antibiotics in human medicine and agriculture. In healthcare settings, unnecessary prescriptions for antibiotics are written for viral infections, which do not need antimicrobial treatment. Also, patients often do not complete their prescribed courses of antibiotics, allowing resistant strains to survive and multiply. According to a detailed report if current trends are allowed to continue, AMR could kill 10 million people annually by the year 2050, making it more deadly than cancer.

Based on the effectiveness of vaccine inoculation and hospital treatment in controlling infectious diseases, and accounting for the complexity of epidemic transmission mechanisms and environmental uncertainties in population dynamics, in this article, we investigate the dynamics of a stochastic SAIR model with vaccination and saturated treatment, where the transmission rate is governed by the logarithmic Ornstein-Uhlenbeck (O-U) process. First, we demonstrate that for any given initial value, there exists a global positive solution. Next, the stationary distribution of the system is obtained through developing complex Lyapunov functions and applying the ergodicity theory of the O-U process. Then, to uncover the statistical properties, the precise expression of the probability density function close to the quasi-equilibrium is given by applying the Routh-Hurwitz criterion and solving the four-dimensional Fokker-Planck equation. We also define sufficient criteria for disease extinction at the local level. Lastly, computer simulations verify that the O-U process has a substantial effect on the dynamics of the model. Notably, our results demonstrate that higher mean-reversion rates coupled with lower volatility intensities substantially mitigate infection outbreaks, potentially informing future therapeutic strategies.

This paper is devoted to the time-space fractional rotating magnetohydrodynamic equations in Besov spaces. By exploiting the interweaving action of the smoothing effects of the fractional Laplacian dissipation and dispersive effects of the Coriolis force involving with the time-fractional evolution mechanism, the existence and uniqueness of global mild solutions are obtained under some smallness conditions by employing Mittag-Leffler operators families and contraction mapping principle. It is worth mentioning that our result permits the initial velocity to be arbitrarily large provided that the rotation parameter is sufficiently large.

In the context of manufacturing logistics, this study sheds light on the difficult task of concurrently optimizing cost, time, influence on sustainability, and spatial efficiency. Specifically, this addresses the integrated challenge of material handling equipment selection and facility space allocation, a crucial decision-making domain where conventional single-objective methodologies frequently overlook vital considerations. While recent research predominantly relies on meta-heuristics and simulation-based solution methodologies, they do not guarantee a global optimum solution space. To effectively address this multifaceted decision environment, a Mixed-Integer Linear Programming (MILP) model is developed and resolved utilizing two distinct scalarization methodologies: the conventional ϵ-constraint method and the augmented ϵ-constraint method (AUGMECON2). The comparative analysis indicates that although both methods effectively identify the Pareto front, the AUGMECON2 approach offers a more robust assurance of solution efficiency by incorporating slack variables. The results illustrate a convex trade-off between capital expenditure and operational flow time, indicating that substantial reductions in time necessitate strategic investments in higher-capacity equipment fleets. Furthermore, the analysis underscores a significant conflict between achieving extreme operational efficiency and adhering to facility design standards, as reducing time or energy consumption beyond a specific point requires deviations from optimal space allocation policies. Ultimately, a “Best Compromise Solution” is determined that harmonizes near-optimal operational efficiency with strict compliance to spatial constraints, providing a resilient framework for sustainable manufacturing logistical planning.

Non-existence of Global Solutions for the Grushin Heat Equation with Nonlocal and Local Nonlinearities

UDC 517.95 We study the problems of well-posedness and stability for fractional linear hyperbolic systems (FLHS) with the Caputo time-fractional derivative. First, the existence and uniqueness are established for the global solution of the FLHS. Then we obtain some polynomial stability results for the FLHS in different Hilbert spaces. Finally, some numerical examples are presented to confirm the theoretical results.

This paper focuses on proving the global existence and uniqueness of solutions to the three-dimensional inhomogeneous incompressible MHD equations provided that the initial density ρ 0 is merely bounded, the initial velocity u 0 and magnetic field belong to the critical Sobolev space H ˙ 1 / 2 ( R 3 ) with the initial data ( u 0 , b 0 ) being sufficiently small in the Besov space B ˙ 2 , ∞ 1 / 2 ( R 3 ) . This result corresponds to the work established in Abidi, Gui and Zhang ( Communications in Partial Differential Equations, 50(6):841-873, 2025).

This paper investigates the absence of globally defined, non-trivial solutions for some fractional differential inequalities of the ψ-Caputo type, with polynomial sources involving fractional derivatives. We rigorously establish these results within an appropriate function space using properties of ψ-fractional integrals and derivatives and the test function technique. To demonstrate the applicability and enhance understanding, we provide three illustrative examples. Our findings broaden the scope of previous literature, encompassing existing results as special cases.

This study addresses the urgent need for innovative strategies to tackle environmental challenges, focusing on the role of private corporations' corporate social responsibility (CSR) initiatives in Nigeria. It examines how firms like Dangote Group and MTNN use CSR, alongside mainstream media agenda-setting functions, to raise environmental awareness and promote sustainability. A literature review contextualizes the theories and assesses how environmental information is disseminated. Findings reveal a significant gap, with limited CSR-led environmental education and public awareness efforts in the media. The study calls for a renewed emphasis on corporate-media synergy, especially in the global south, to enhance private sector contributions to global environmental solutions.

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: ∂2u∂t2−div(K(‖σ∇u‖L2(Ω)2)Aσ(x)∇u)+M(‖u‖L2(Ω)2)u−div(ζ(t)Aσ(x)∇∂u∂t)+d0(t)∂u∂t+Dr(x,t;∂u∂t)=G(u), where u(x,t) is the state function, M and K are the nonlocal Kirchhoff operators and the nonlinear operator G(u) corresponds to a logarithmic source term. The symmetric tensor Aσ describes the anisotropic behavior and processes of the system, and the operator Dr represents the multiple time-varying mixed delays related to velocity ∂u∂t. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms.

This paper presents the design, development, and evaluation of EcoTrack, an Android-based carbon footprint tracking application specifically tailored for the Zambian context. The application addresses critical gaps in existing environmental monitoring tools by focusing on locally relevant emission sources, particularly biomass fuels, and implementing offline-first architecture suitable for connectivity-constrained environments. Developed using Java and the Room Persistence Library, EcoTrack employs a Model-View-ViewModel (MVVM) architecture to ensure robust performance and maintainability. The Application’s calculation engine integrates International Panel on Climate Change (IPCC) standards for fossil fuels with United States Environmental Protection Agency (EPA) factors for biomass fuels. Rigorous testing across 150 scenarios demonstrated calculation accuracies of 98.2% for petrol (95% CI: 97.8-98.6%), 97.9% for diesel (95% CI: 97.4-98.4%), and 96.5% for charcoal (95% CI: 95.8-97.2%). User studies with 30 Zambian participants yielded a System Usability Scale (SUS) score of 82.5 (excellent range) and 94% task completion rate. Notably, 96% of users confirmed the relevance of charcoal tracking, addressing a significant omission in existing global solutions. The research demonstrates that context-aware mobile applications can effectively bridge the gap between global environmental standards and local user needs in developing regions, providing a replicable model for similar applications across sub-Saharan Africa.

We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential operator, which provides a spectral decomposition of L 2 ( M ) L^2(M) into finite-dimensional eigenspaces. This framework allows us to characterize these global properties through asymptotic estimates on the matrix symbols of the operators. Additionally, for systems of normal strongly invariant operators, we derive an explicit solution formula and establish sufficient conditions for global hypoellipticity and solvability in terms of their eigenvalues.

ABSTRACT In this paper, we investigate a nonlocal diffusion SIR epidemic model with double free boundaries, where the infection rate and the recovery rate have been affected by media coverage and the number of hospital beds, respectively. We first give the existence and uniqueness of a global solutions, and then study the long‐time behaviors and sufficient conditions for the disease spreading and vanishing.

Modular multilevel converter (MMC) is widely employed in high-voltage direct current (HVDC) systems for the long-distance renewable energy transmission, where the larger submodule (SM) capacitors significantly increase its size, weight and cost. Conventional capacitor voltage fluctuation suppression methods, such as composite harmonic injection (CHI) strategies, can achieve lightweight MMC. However, these approaches often neglect the dynamic constraints between harmonic injection parameters and their coupled effect on modulation wave, which not only leads to suboptimal global solutions but also increases the risk of system overshoot. Therefore, this paper proposes a comprehensive CHI parameters optimization method to minimize capacitor voltage fluctuations, thereby allowing for a smaller SM capacitor. First, the analytical expression of SM average capacitor voltage is developed, incorporating the injected second-order harmonic circulating current and third-order harmonic voltage. On this basis, an objective function is defined to minimize the sum of the fundamental and second-order harmonic components of the average capacitor voltage, with the harmonic injection parameters and modulation index as optimization variables. Then, these parameters are optimized using a particle swarm optimization (PSO) algorithm, where their constraints are set to prevent modulation wave overshoot and additional power loss. Finally, the optimization method is validated through a ±500 kV, 1500 MW MMC-HVDC system under various power conditions in PSCAD/EMTDC (version 4.6.3). In addition, simulation results demonstrate that the proposed method can achieve a 13.33% greater reduction in SM capacitance value compared to conventional strategies.