Communications in Mathematical Sciences

Article	Citations
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drif	30
Entropy admissibility of the limit solution for a nonlocal model of traffic flow	22
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities	20
Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime	18
Identification of time-varying source term in time-fractional diffusion equations	12
Deep fictitious play for stochastic differential games	12
Discrete maximum principle of a high order finite difference scheme for a generalized Allen–Cahn equation	11
Analytically pricing variance swaps in commodity derivative markets under stochastic convenience yields	11
Unidirectional flocks in hydrodynamic Euler alignment system II: singular models	10
Global well-posedness of the stochastic Camassa–Holm equation	10
Numerical approximations and error analysis of the Cahn–Hilliard equation with dynamic boundary conditions	9
Wavenumber-explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers	9
A fully well-balanced scheme for shallow water equations with Coriolis force	9
Energy stability of variable-step L1-type schemes for time-fractional Cahn–Hilliard model	9
Complete monotonicity-preserving numerical methods for time fractional ODEs	8
Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag	8
Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems	8
Global smooth solutions to the 3D non-resistive MHD equations with low regularity axisymmetric data	8
Nonlocal approaches for multilane traffic models	7
Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case	7
Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations	7
A sharp critical threshold for a traffic flow model with look-ahead dynamics	7
A second-order accurate, energy stable numerical scheme for the one-dimensional porous medium equation by an energetic variational approach	7
An ellipsoidal statistical model for a monoatomic and a polyatomic gas mixture	6
A general framework for nonlocal Neumann problems	6

Efficient numerical scheme for the anisotropic modified phase-field crystal model with a strong nonlinear vacancy potential	6
On entropic solutions to conservation laws coupled with moving bottlenecks	6
An energy stable finite difference scheme for the Ericksen–Leslie system with penalty function and its optimal rate convergence analysis	6
Degenerate Cahn–Hilliard and incompressible limit of a Keller–Segel model	6
On the continuous time limit of ensemble square root filters	6
High energy blowup and blowup time for a class of semilinear parabolic equations with singular potential on manifolds with conical singularities	6
Complexity of randomized algorithms for underdamped Langevin dynamics	6
Dual quaternion matrices in multi-agent formation control	6
Fast Sinkhorn I: An $O(N)$ algorithm for the Wasserstein-1 metric	6
Strong solutions to a modified Michelson-Sivashinsky equation	5
Hypocoercivity of stochastic Galerkin formulations for stabilization of kinetic equations	5
Analysis of a cross-diffusion model for rival gangs interaction in a city	5
Kinetic and hydrodynamic models for the relativistic Cucker–Smale ensemble and emergent behaviors	5
Wave breaking for a model equation for shallow water waves of moderate amplitude	5
Local error of a splitting scheme for a nonlinear Schrödinger-type equation with random dispersion	5
Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions	5
Mass-energy threshold dynamics for dipolar quantum gases	5
A Fourier collocation method for Schrödinger–Poisson system with perfectly matched layer	5
The Fourier Discrepancy Function	5
An efficient data-driven solver for Fokker–Planck equations: algorithm and analysis	5
Local wellposedness of quasilinear Maxwell equations with conservative interface conditions	5
A fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations	4
A low Mach two-speed relaxation scheme for the compressible Euler equations with gravity	4
On variational principles for polarization responses in electromechanical systems	4
The Bramson correction for integro-differential Fisher–KPP equations	4
A generalized mean-field game model for the dynamics of pedestrians with limited predictive abilities	4
Continuum limits for adaptive network dynamics	4
Universal approximation of symmetric and anti-symmetric functions	4
Long term spatial homogeneity for a chemotaxis model with local sensing and consumption	4
An MBO scheme for clustering and semi-supervised clustering of signed networks	4
Propagator norm and sharp decay estimates for Fokker–Planck equations with linear drift	4
Emergence of stochastic flocking for the discrete Cucker–Smale model with randomly switching topologies	4
Global dynamics below the ground states for NLS under partial harmonic confinement	4
Decoherence rhapsody in the photosynthesis process	3
Consistency analysis of bilevel data-driven learning in inverse problems	3
Tensor PDE model of biological network formation	3
Existence, regularity and weak-strong uniqueness for three-dimensional Peterlin viscoelastic model	3
On dissipative solutions to a simplified hyperbolic Ericksen–Leslie system of liquid crystals	3
Sobolev training for physics-informed neural networks	3
Error analysis of Galerkin spectral methods for nonlinear optimal control problems with integral control constraint	3
Blowup for $C^1$ solutions of compressible Euler equations with time-dependent damping	3
Error estimate of the nonuniform $L1$ type formula for the time fractional diffusion-wave equation	3
Galerkin spectral methods for an elliptic optimal control problem with $L^2$-norm state constraint	3
On the properties of affine solutions of cold plasma equations	3
On homogenization of the Landau–Lifshitz equation with rapidly oscillating material coefficient	3
A regularity criterion for the Navier–Stokes equations via one diagonal entry of the velocity gradient	3
On the sedimentation of a droplet in Stokes flow	3
An improved small data theorem for the Vlasov–Poisson system	3
Radon measure solutions for steady hypersonic-limit Euler flows passing two-dimensional finite non-symmetric obstacles and interactions of free concentration layers	3
Stabilized exponential time differencing schemes for the convective Allen–Cahn equation	3

Improved uniform error bound on the time-splitting method for the long-time dynamics of the fractional nonlinear Schrödinger equation	3
ST-SVD factorization and s-diagonal tensors	3
On two-dimensional steady hypersonic-limit Euler flows passing ramps and radon measure solutions of compressible Euler equations	3
Stability of the planar rarefaction wave to three-dimensional compressible model of viscous ions motion	2
On connection among quantum-inspired algorithms of the Ising model	2
Scattering for 3D quantum Zakharov system in $L^2$	2
The Cauchy problem for a non strictly hyperbolic $3 \times 3$ system of conservation laws arising in polymer flooding	2
Microscopic and macroscopic traffic flow models including random accidents	2
Traveling waves in a Keller–Segel model with logistic growth	2
Reaction-diffusion equations derived from kinetic models and their Turing instability	2
Some models for the interaction of long and short waves in dispersive media. Part II: Well-posedness	2
Kinetic model for myxobacteria with directional diffusion	2
Analysis of the role of convection in a system describing the tumor-induced angiogenesis	2
On the convergence of frozen Gaussian approximation for linear non-strictly hyperbolic systems	2
A second-order well-balanced Lagrange-projection numerical scheme for shallow water Exner equations in 1D and 2D	2
Dynkin game for callable-puttable convertible bonds: the valuation and sensitivity analysis	2
Normalized Goldstein-type local minimax method for finding multiple unstable solutions of semilinear elliptic PDEs	2
Low-Mach type approximation of the Navier–Stokes system with temperature and salinity for free surface flows	2
Stability of equilibria to the model for non-isothermal electrokinetics	2
Numerical methods for stochastic differential equations based on Gaussian mixture	2
The existence of compressible subsonic impinging jet flow in an arbitrary nozzle	2
Initial mixed-boundary value problem for anisotropic fractional degenerate parabolic equations	2
Existence and uniqueness for a stationary hybrid quantum hydrodynamical model with general pressure functional	2
Global solutions of 3D tropical climate model with finite energy	2
A Wasserstein norm for signed measures, with application to non-local transport equation with source term	2
Convergence analysis of structure-preserving numerical methods based on Slotboom transformation for the Poisson–Nernst–Planck equations	2
Lake equations with an evanescent or emergent island	2
A Cahn-Hilliard model coupled to viscoelasticity with large deformations	2
Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case	2
Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme	2
Selection and mutation in a shifting and fluctuating environment	2
Vanishing viscosity limit for compressible magnetohydrodynamic equations with transverse background magnetic field	2
Numerical evidence of exponential mixing by alternating shear flows	2
Interaction of the elementary waves for shallow water equations with discontinuous topography	2
Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimension	2
Cucker–Smale flocking under hierarchical leadership with time-delay and a free-will leader	2
Recovery of a distributed order fractional derivative in an unknown medium	2
Large time behavior for a Hamilton–Jacobi equation in a critical coagulation-fragmentation model	1
A note on optimization formulations of Markov decision processes	1
A nonlocal model of elliptic equation with jump coefficients on manifold	1
Conservative semi-Lagrangian schemes for a general consistent BGK model for inert gas mixtures	1
Global well-posedness and decay of the low-regularity solution to the 3D density-dependent magnetohydrodynamic equations with vacuum	1
Regularized least square kernel regression for streaming data	1
The Cahn-Hilliard-Boussinesq system with singular potential	1
Global mild solutions of the non-cutoff Vlasov–Poisson–Boltzmann system	1
Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate	1
Existence of polynomial attractor for a class of extensible beams with nonlocal weak damping	1
Reproducing activation function for deep learning	1
Unified asymptotic analysis and numerical simulations of singularly perturbed linear differential equations under various nonlocal boundary effects	1
Interior eigensolver for sparse Hermitian definite matrices based on Zolotarev’s functions	1
On bifurcation of self-similar solutions of the stationary Navier–Stokes equations	1
Global solvability to a cancer invasion model with remodeling of ECM and porous medium diffusion	1
Nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising from radiation hydrodynamics	1
Analysis of the time-domain PML problem for the electromagnetic scattering by periodic structures	1
Blow-up time of strong solutions to a biological network formation model in high space dimensions	1
Global regularity and time decay for the 2D magneto-micropolar system with fractional dissipation and partial magnetic diffusion	1
Relative entropy in diffusive relaxation for a class of discrete velocities BGK models	1
Exponential synchronization of Kuramoto oscillators with time delayed coupling	1
On uniform second-order nonlocal approximations to diffusion and subdiffusion equations with nonlocal effect parameter	1
Limiting behaviors of high dimensional stochastic spin ensembles	1
Location of concentrated vortices in planar steady Euler flows	1
Long time existence of the Boussinesq equation with large initial data in $\mathbb{R}^n$	1
Thermodynamically consistent dynamic boundary conditions of phase field models	1
Existence and decay of global strong solutions to the nonhomogeneous incompressible liquid crystal system with vacuum and density-dependent viscosity	1
Fokker–Planck modeling of many-agent systems in swarm manufacturing: asymptotic analysis and numerical results	1
Second-order accurate Dirichlet boundary conditions for linear nonlocal diffusion problems	1
Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations	1
Boundary layer and asymptotic stability for the Navier–Stokes–Poisson equations with nonslip boundary conditions	1
Stability and convergence of a variable-step stabilized BDF2 stepping for the MBE model with slope selection	1
Rarefied gas dynamics with external fields under specular reflection boundary condition	1
A quantitative version of the transversality theorem	1
Time-periodic solution for an incompressible magnetohydrodynamic system with an external force in $\mathbb{R}^N$	1
Implicit-explicit Runge-Kutta methods for Landau-Lifshitz equation with arbitrary damping	1
Gamma convergence for the de Gennes–Cahn–Hilliard energy	1
Optimal large time behavior of the compressible bipolar Navier–Stokes–Poisson system	1
Autonomous vehicles driving traffic: The Cauchy problem	1
Invariant domain preserving central schemes for nonlinear hyperbolic systems	1
Global-in-time stability of ground states of a pressureless hydrodynamic model of collective behaviour	1
An optimal design of random surfaces in solar cells via mini-batch stochastic gradient approach	1
An asymptotic preserving scheme for Lévy-Fokker-Planck equation with fractional diffusion limit	1

On the gradient flow structure of the isotropic Landau equation	1
Global existence and large time behavior of strong solutions for nonhomogeneous heat conducting Navier–Stokes equations with large initial data and vacuum	1
Global existence for quasilinear degenerate two-species chemotaxis system with small initial data	1
A derivative-free conjugate gradient method for large-scale nonlinear systems of monotone equations	1
Non-uniqueness of transonic shock solutions to non-isentropic Euler–Poisson system	1
Optimal sample complexity of subgradient descent for amplitude flow via non-Lipschitz matrix concentration	1
$L^\infty$ continuation principle for two-dimensional compressible nematic liquid crystal flows	1
Global strong solutions for planar full compressible Hall-MHD equations with large initial data	1
Global convergence of triangularized orthogonalization-free method	1
Heterogeneous multiscale methods for rough-wall laminar viscous flow	1
Existence of smooth solutions to the Landau–Fermi–Dirac equation with Coulomb potential	1
Low Mach number limit of the full compressible mhd equations with Cattaneo’s heat transfer law	1
A variational approach for price formation models in one dimension	1
A Cahn–Hilliard model with a proliferation term for the proliferative-to-invasive transition of hypoxic glioma cells	1
A finite element method for Dirichlet boundary control of elliptic partial differential equations	1
Approximations of the stochastic 3D Navier–Stokes equations with damping	1
Lack of exact controllability of a higher-order BBM system	1
Energy method for the Boltzmann equation of monatomic gaseous mixtures	1
On anisotropic non-Lipschitz restoration model: lower bound theory and iterative algorithm	1
A quadratic spline projection method for computing stationary densities of random maps	1
Energy conservation for 2D Euler with vorticity in $L (\operatorname{log} L)^\alpha$	1
Homogenization of a transmission problem with sign-changing coefficients and interfacial flux jump	1
Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe	1
Van der Waals interactions between two hydrogen atoms: The next orders	1
Global solutions to rotating motion of isentropic flows with cylindrical symmetry	1
The nonlinear Schrödinger equation with white noise dispersion on quantum graphs	1
Asymptotic behavior of solutions to the outflow problem for the compressible Navier–Stokes–Maxwell equations	1
Design of a mode converter using thin resonant ligaments	1
Global existence and stability of time-periodic solution to isentropic compressible Euler equations with source term	1
Sub-exponential convergence to steady-states for 1-D Euler–Poisson equations with time-dependent damping	1
Adaptive central-upwind scheme on triangular grids for the Saint–Venant system	1