Mathematical Models & Methods in Applied Sciences

Article	Citations
A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world	103
Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision	55
What is life? A perspective of the mathematical kinetic theory of active particles	48
Coupling kinetic theory approaches for pedestrian dynamics and disease contagion in a confined environment	44
Towards a mathematical theory of behavioral human crowds	39
Convergence of a first-order consensus-based global optimization algorithm	30
A multilayer network model of the coevolution of the spread of a disease and competing opinions	29
Global boundedness and asymptotic behavior in a quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source	27
Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit	27
A multiscale network-based model of contagion dynamics: Heterogeneity, spatial distancing and vaccination	27
On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case	27
Global bounded solution of the higher-dimensional forager–exploiter model with/without growth sources	25
Instability of the abstract Rayleigh–Taylor problem and applications	24
A phase-field-based graded-material topology optimization with stress constraint	24
Hyperbolic compartmental models for epidemic spread on networks with uncertain data: Application to the emergence of COVID-19 in Italy	23
Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka–Volterra competitive kinetics	23
Polynomial preserving virtual elements with curved edges	23
Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth	22
Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects	21
From particle swarm optimization to consensus based optimization: Stochastic modeling and mean-field limit	21
Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties	21
Element-splitting-invariant local-length-scale calculation in B-Spline meshes for complex geometries	21
Global radial renormalized solution to a producer–scrounger model with singular sensitivities	18
Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations	18
Repulsive chemotaxis and predator evasion in predator–prey models with diffusion and prey-taxis	17

Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra	17
Asymptotic dynamics on a chemotaxis-Navier–Stokes system with nonlinear diffusion and inhomogeneous boundary conditions	16
Global solvability and eventual smoothness in a chemotaxis-fluid system with weak logistic-type degradation	15
A data-driven epidemic model with social structure for understanding the COVID-19 infection on a heavily affected Italian province	15
Disease contagion models coupled to crowd motion and mesh-free simulation	15
A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations	15
Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation	15
Boundary layer mesh resolution in flow computation with the Space–Time Variational Multiscale method and isogeometric discretization	15
Flow computation with the Space–Time Isogeometric Analysis and higher-order basis functions in time	14
Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: From subcellular dynamics to macroscopic PDEs with multiple taxis	14
Control of COVID-19 outbreak using an extended SEIR model	14
Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials	14
Coarse-graining via EDP-convergence for linear fast-slow reaction systems	14
From particles to firms: on the kinetic theory of climbing up evolutionary landscapes	13
An approach to congestion analysis in crowd dynamics models	13
A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems	13
A C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraints	13
A kinetic theory approach for 2D crowd dynamics with emotional contagion	13
Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations	12
On fully decoupled MSAV schemes for the Cahn–Hilliard–Navier–Stokes model of two-phase incompressible flows	12
Asymptotic analysis for a Vlasov–Fokker–Planck/Navier–Stokes system in a bounded domain	12
Simulating air blast on concrete structures using the volumetric penalty coupling of isogeometric analysis and peridynamics	12
The curl–curl conforming virtual element method for the quad-curl problem	12
Vorticity-stabilized virtual elements for the Oseen equation	12
A kinetic theory approach for modelling tumour and macrophages heterogeneity and plasticity during cancer progression	12
Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces	12
A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh	12
Global solvability and asymptotic stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with indirect signal production	12
Negligibility of haptotaxis effect in a chemotaxis–haptotaxis model	12
Social climbing and Amoroso distribution	11
The one-phase fractional Stefan problem	11
Hybridization of the virtual element method for linear elasticity problems	11
Asymptotic profile of a two-dimensional Chemotaxis–Navier–Stokes system with singular sensitivity and logistic source	11
DG approach to large bending plate deformations with isometry constraint	11
On a nonlocal Cahn–Hilliard model permitting sharp interfaces	10
Time-fractional Moore–Gibson–Thompson equations	10
Transmission dynamics and quarantine control of COVID-19 in cluster community: A new transmission-quarantine model with case study for diamond princess	10
Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains	10
Nematic alignment of self-propelled particles: From particle to macroscopic dynamics	9
Human behavioral crowds review, critical analysis and research perspectives	9
Virus models in complex frameworks: Towards modeling space patterns of SARS-CoV-2 epidemics	9
A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution	9
Equilibrium analysis of an immersed rigid leaflet by the virtual element method	9
Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary	9
Generalized solutions to bounded-confidence models	8
Condition number bounds for IETI-DP methods that are explicit in h and p	8
Individual-based Markov model of virus diffusion: Comparison with COVID-19 incubation period, serial interval and regional time series	8
Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models	8
The existence and stability of spike solutions for a chemotax is system modeling crime pattern formation	8
Geometric linearization of theories for incompressible elastic materials and applications	8

Efficient, second-order in time, and energy stable scheme for a new hydrodynamically coupled three components volume-conserved Allen–Cahn phase-field model	8
Hydrodynamic limit of a coupled Cucker–Smale system with strong and weak internal variable relaxation	7
Lagrange multiplier approach to unilateral indentation problems: Well-posedness and application to linearized viscoelasticity with non-invertible constitutive response	7
Multiple asymptotics of kinetic equations with internal states	7
Statistical solutions of the incompressible Euler equations	7
Computing oscillatory solutions of the Euler system via ?-convergence	7
Isogeometric discretization methods in computational fluid mechanics	7
Final size and convergence rate for an epidemic in heterogeneous populations	7
Model predictive control with random batch methods for a guiding problem	7
Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence	7
Error estimates of local energy regularization for the logarithmic Schrödinger equation	7
Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems	7
Doubly nonlinear stochastic evolution equations	7
Analysis-aware defeaturing: Problem setting and a posteriori estimation	6
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics	6
Immersed virtual element methods for electromagnetic interface problems in three dimensions	6
A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity	6
Chemotaxis systems in complex frameworks: Pattern formation, qualitative analysis and blowup prevention	6
Global regularity for a 1D Euler-alignment system with misalignment	6
Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction	6
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods	6
Normalized solutions with positive energies for a coercive problem and application to the cubic–quintic nonlinear Schrödinger equation	6
Fluid–structure interaction modeling with nonmatching interface discretizations for compressible flow problems: Computational framework and validation study	6
Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media	6
Some aspects of the inertial spin model for flocks and related kinetic equations	6
Generalized solution and eventual smoothness in a logarithmic Keller–Segel system for criminal activities	6
On the dynamic slip boundary condition for Navier–Stokes-like problems	6
Kinetic modeling of coupled epidemic and behavior dynamics: The social impact of public policies	5
Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread	5
Cross-diffusion models in complex frameworks from microscopic to macroscopic	5
A kinetic modeling of crowd evacuation with several groups in complex venues	5
On a two-species chemotaxis system with indirect signal production and general competition terms	5
Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks	5
Uniform-in-time error estimate of the random batch method for the Cucker–Smale model	5
Point defects in tight binding models for insulators	5
On the critical exponent of the one-dimensional Cucker–Smale model on a general graph	5
On the optimality of the rock-salt structure among lattices with charge distributions	5
Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow	5
Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system	5
Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness	5
Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis	5
Approximation of surface diffusion flow: A second-order variational Cahn–Hilliard model with degenerate mobilities	5
A general cell–fluid Navier–Stokes model with inclusion of chemotaxis	5
A parabolic local problem with exponential decay of the resonance error for numerical homogenization	4
Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation	4
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions	4
Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises	4
Variational multiscale method stabilization parameter calculated from the strain-rate tensor	4
Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications	4
A unified framework for Navier–Stokes Cahn–Hilliard models with non-matching densities	4
Interpolation and stability estimates for edge and face virtual elements of general order	4
Boundedness and asymptotic stabilization in a two-dimensional Keller–Segel–Navier–Stokes system with sub-logistic source	4
Atomistic origins of continuum dislocation dynamics	4
A mean-field approach to self-interacting networks, convergence and regularity	4
Linearized von Kármán theory for incompressible magnetoelastic plates	4
Viscoelastic Cahn–Hilliard models for tumor growth	4
On the mathematical theory of behavioral swarms emerging collective dynamics	4
A fast cardiac electromechanics model coupling the Eikonal and the nonlinear mechanics equations	4
Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles	4
Coupling compartmental models with Markov chains and measure evolution equations to capture virus mutability	4
An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations	4
On effects of the nonlinear signal production to the boundedness and finite-time blow-up in a flux-limited chemotaxis model	4
Construction of boundary conditions for hyperbolic relaxation approximations I: The linearized Suliciu model	4
Remarks on Poincaré and interpolation estimates for Truncated Hierarchical B-splines	3
Existence and stability of symmetric and asymmetric patterns for the half-Laplacian Gierer–Meinhardt system in one-dimensional domain	3
Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers	3
Tangential Navier–Stokes equations on evolving surfaces: Analysis and simulations	3
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications	3
Density-induced consensus protocol	3
Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity	3
A stochastic model of grain boundary dynamics: A Fokker–Planck perspective	3
A robust VEM-based approach for flow simulations in poro-fractured media	3
Critical mass for Keller–Segel systems with supercritical nonlinear sensitivity	3
A multi-agent approach to the impact of epidemic spreading on commercial activities	3
Isogeometric large-eddy simulations of turbulent particle-laden flows	3
Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases	3
Where to cut to delay a pandemic with minimum disruption? mathematical analysis based on the SIS model	3
Newtonian repulsion and radial confinement: Convergence toward steady state	3
Sharp discontinuous traveling waves in a hyperbolic Keller–Segel equation	3
The synergy between two threats: Disinformation and COVID-19	3

Global existence of weak solutions to the incompressible Vlasov–Navier–Stokes system coupled to convection–diffusion equations	3
Equilibria of an aggregation model with linear diffusion in domains with boundaries	3
Combined dynamics of magnetization and particle rotation of a suspended superparamagnetic particle in the presence of an orienting field: Semi-analytical and numerical solution	3
On the formulation of size-structured consumer resource models (with special attention for the principle of linearized stability)	3
Fluid models with phase transition for kinetic equations in swarming	3
Stability for the training of deep neural networks and other classifiers	3
H(curl2)-conforming quadrilateral spectral element method for quad-curl problems	3
Shape programming of a magnetic elastica	3
Pressure-relaxation limit for a one-velocity Baer–Nunziato model to a Kapila model	3
Energy minimizing twinning with variable volume fraction, for two nonlinear elastic phases with a single rank-one connection	3
Elasto-plastic evolution of single crystals driven by dislocation flow	3
Stationary Cahn–Hilliard–Navier–Stokes equations for the diffuse interface model of compressible flows	3
Preconditioning the EFIE on screens	3
Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method	3
The stationary Boussinesq problem under singular forcing	3
On nonlinear problems of parabolic type with implicit constitutive equations involving flux	3
Isogeometric variational multiscale modeling of stably stratified flow over complex terrains	3
Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids	3