Mathematical Models & Methods in Applied Sciences

Article	Citations
Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision	69
What is life? A perspective of the mathematical kinetic theory of active particles	60
Towards a mathematical theory of behavioral human crowds	51
A multilayer network model of the coevolution of the spread of a disease and competing opinions	34
A multiscale network-based model of contagion dynamics: Heterogeneity, spatial distancing and vaccination	32
Global boundedness and asymptotic behavior in a quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source	31
Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit	30
From particle swarm optimization to consensus based optimization: Stochastic modeling and mean-field limit	26
Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka–Volterra competitive kinetics	25
Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth	25
Hyperbolic compartmental models for epidemic spread on networks with uncertain data: Application to the emergence of COVID-19 in Italy	25
Human behavioral crowds review, critical analysis and research perspectives	24
Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations	23
A data-driven epidemic model with social structure for understanding the COVID-19 infection on a heavily affected Italian province	20
On fully decoupled MSAV schemes for the Cahn–Hilliard–Navier–Stokes model of two-phase incompressible flows	19
Control of COVID-19 outbreak using an extended SEIR model	18
Boundary layer mesh resolution in flow computation with the Space–Time Variational Multiscale method and isogeometric discretization	17
Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: From subcellular dynamics to macroscopic PDEs with multiple taxis	17
A kinetic theory approach for 2D crowd dynamics with emotional contagion	17
Disease contagion models coupled to crowd motion and mesh-free simulation	17
Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces	16
A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations	16
Flow computation with the Space–Time Isogeometric Analysis and higher-order basis functions in time	16
Vorticity-stabilized virtual elements for the Oseen equation	16
A C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraints	16

Negligibility of haptotaxis effect in a chemotaxis–haptotaxis model	16
The curl–curl conforming virtual element method for the quad-curl problem	16
Time-fractional Moore–Gibson–Thompson equations	16
Repulsive chemotaxis and predator evasion in predator–prey models with diffusion and prey-taxis	16
Asymptotic analysis for a Vlasov–Fokker–Planck/Navier–Stokes system in a bounded domain	15
Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations	15
On a nonlocal Cahn–Hilliard model permitting sharp interfaces	15
Global solvability and asymptotic stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with indirect signal production	15
A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh	14
Simulating air blast on concrete structures using the volumetric penalty coupling of isogeometric analysis and peridynamics	14
Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary	14
A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems	14
Hybridization of the virtual element method for linear elasticity problems	14
DG approach to large bending plate deformations with isometry constraint	13
A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution	13
Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains	13
The one-phase fractional Stefan problem	12
Asymptotic profile of a two-dimensional Chemotaxis–Navier–Stokes system with singular sensitivity and logistic source	12
A unified framework for Navier–Stokes Cahn–Hilliard models with non-matching densities	11
Statistical solutions of the incompressible Euler equations	11
Transmission dynamics and quarantine control of COVID-19 in cluster community: A new transmission-quarantine model with case study for diamond princess	10
Model predictive control with random batch methods for a guiding problem	10
Geometric linearization of theories for incompressible elastic materials and applications	10
Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction	10
Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models	10
Virus models in complex frameworks: Towards modeling space patterns of SARS-CoV-2 epidemics	9
Efficient, second-order in time, and energy stable scheme for a new hydrodynamically coupled three components volume-conserved Allen–Cahn phase-field model	9
Kinetic modeling of coupled epidemic and behavior dynamics: The social impact of public policies	9
Viscoelastic Cahn–Hilliard models for tumor growth	9
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics	9
Error estimates of local energy regularization for the logarithmic Schrödinger equation	9
Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems	9
Equilibrium analysis of an immersed rigid leaflet by the virtual element method	9
Isogeometric discretization methods in computational fluid mechanics	9
Individual-based Markov model of virus diffusion: Comparison with COVID-19 incubation period, serial interval and regional time series	9
Normalized solutions with positive energies for a coercive problem and application to the cubic–quintic nonlinear Schrödinger equation	9
Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence	8
From Herbert A. Simon’s legacy to the evolutionary artificial world with heterogeneous collective behaviors	8
Generalized solutions to bounded-confidence models	8
Computing oscillatory solutions of the Euler system via ?-convergence	8
Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles	8
Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks	8
Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media	8
Lagrange multiplier approach to unilateral indentation problems: Well-posedness and application to linearized viscoelasticity with non-invertible constitutive response	8
Final size and convergence rate for an epidemic in heterogeneous populations	8
Hydrodynamic limit of a coupled Cucker–Smale system with strong and weak internal variable relaxation	7
On some smooth symmetric transonic flows with nonzero angular velocity and vorticity	7
On effects of the nonlinear signal production to the boundedness and finite-time blow-up in a flux-limited chemotaxis model	7
Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications	7
Global regularity for a 1D Euler-alignment system with misalignment	7

Tangential Navier–Stokes equations on evolving surfaces: Analysis and simulations	7
Kinetic modeling of a leader–follower system in crowd evacuation with collective learning	7
On the dynamic slip boundary condition for Navier–Stokes-like problems	7
Analysis-aware defeaturing: Problem setting and a posteriori estimation	7
Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis	7
Immersed virtual element methods for electromagnetic interface problems in three dimensions	7
Variational multiscale method stabilization parameter calculated from the strain-rate tensor	7
Numerical modeling of the brain poromechanics by high-order discontinuous Galerkin methods	6
A kinetic modeling of crowd evacuation with several groups in complex venues	6
Cross-diffusion models in complex frameworks from microscopic to macroscopic	6
Fluid–structure interaction modeling with nonmatching interface discretizations for compressible flow problems: Computational framework and validation study	6
An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations	6
Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises	6
A fast cardiac electromechanics model coupling the Eikonal and the nonlinear mechanics equations	6
Generalized solution and eventual smoothness in a logarithmic Keller–Segel system for criminal activities	6
H(curl2)-conforming quadrilateral spectral element method for quad-curl problems	6
Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread	6
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods	6
Point defects in tight binding models for insulators	6
A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity	6
Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation	6
Uniform-in-time error estimate of the random batch method for the Cucker–Smale model	5
Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces	5
BV solutions for a hydrodynamic model of flocking-type with all-to-all interaction kernel	5
Coupling compartmental models with Markov chains and measure evolution equations to capture virus mutability	5
Consensus-based optimization via jump-diffusion stochastic differential equations	5
On nonlinear problems of parabolic type with implicit constitutive equations involving flux	5
Epidemics and society — A multiscale vision from the small world to the globally interconnected world	5
Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity	5
Boundedness and asymptotic stabilization in a two-dimensional Keller–Segel–Navier–Stokes system with sub-logistic source	5
Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains	5
On the optimality of the rock-salt structure among lattices with charge distributions	5
On the formulation of size-structured consumer resource models (with special attention for the principle of linearized stability)	5
The stationary Boussinesq problem under singular forcing	5
Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system	5
A parabolic local problem with exponential decay of the resonance error for numerical homogenization	5
Pressure-relaxation limit for a one-velocity Baer–Nunziato model to a Kapila model	5
Consensus formation in first-order graphon models with time-varying topologies	5
Existence of multi-spikes in the Keller–Segel model with logistic growth	5
Approximation of surface diffusion flow: A second-order variational Cahn–Hilliard model with degenerate mobilities	5
Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity	5
On a two-species chemotaxis system with indirect signal production and general competition terms	5
Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids	4
Interpolation and stability estimates for edge and face virtual elements of general order	4
Existence and stability of symmetric and asymmetric patterns for the half-Laplacian Gierer–Meinhardt system in one-dimensional domain	4
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions	4
Bound-preserving finite element approximations of the Keller–Segel equations	4
Modeling and numerical simulations of multilane vehicular traffic by active particles methods	4
On the optimal control of propagation fronts	4
On the mathematical theory of behavioral swarms emerging collective dynamics	4
The virtual element method for the 3D resistive magnetohydrodynamic model	4
Biological modeling with nonlocal advection–diffusion equations	4
A mean-field approach to self-interacting networks, convergence and regularity	4
Linearized von Kármán theory for incompressible magnetoelastic plates	4
A multi-agent approach to the impact of epidemic spreading on commercial activities	4
On the stochastic singular Cucker–Smale model: Well-posedness, collision-avoidance and flocking	4
Atomistic origins of continuum dislocation dynamics	4
The synergy between two threats: Disinformation and COVID-19	4
Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method	4
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications	3
The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem	3
A stochastic model of grain boundary dynamics: A Fokker–Planck perspective	3
Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications	3
Kinetic compartmental models driven by opinion dynamics: Vaccine hesitancy and social influence	3
Entropy dissipation and propagation of chaos for the uniform reshuffling model	3
Inf–sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment	3
Global boundedness in a 2D chemotaxis-Navier–Stokes system with flux limitation and nonlinear production	3
Differential games for crowd dynamics and applications	3
Remarks on Poincaré and interpolation estimates for Truncated Hierarchical B-splines	3
Newtonian repulsion and radial confinement: Convergence toward steady state	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
New primal and dual-mixed finite element methods for stable image registration with singular regularization	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
Asymptotic behavior of a three-dimensional haptotactic cross-diffusion system modeling oncolytic virotherapy	3
Quantitative observability for the Schrödinger and Heisenberg equations: An optimal transport approach	3
Well-posedness for SQG sharp fronts with unbounded curvature	3
Stability for the training of deep neural networks and other classifiers	3
Convergence of a particle method for a regularized spatially homogeneous Landau equation	3
Isogeometric large-eddy simulations of turbulent particle-laden flows	3

Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers	3
Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases	3
Populations facing a nonlinear environmental gradient: Steady states and pulsating fronts	3
A nonlinear bending theory for nematic LCE plates	3
Asymptotic analysis of deformation behavior in high-contrast fiber-reinforced materials: Rigidity and anisotropy	3
Structured population models on Polish spaces: A unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of heterogeneous populations	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
Global small solutions to the 3D compressible viscous non-resistive MHD system	3
Isogeometric variational multiscale modeling of stably stratified flow over complex terrains	3
L1-Theory for Hele-Shaw flow with linear drift	3
On an elastic strain-limiting special Cosserat rod model	3
Shape programming of a magnetic elastica	3
Where to cut to delay a pandemic with minimum disruption? mathematical analysis based on the SIS model	3
Sharp discontinuous traveling waves in a hyperbolic Keller–Segel equation	3
Regular solutions of chemotaxis-consumption systems involving tensor-valued sensitivities and Robin type boundary conditions	3