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	25
Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime	16
Entropy admissibility of the limit solution for a nonlocal model of traffic flow	15
Deep fictitious play for stochastic differential games	12
Discrete maximum principle of a high order finite difference scheme for a generalized Allen–Cahn equation	10
Identification of time-varying source term in time-fractional diffusion equations	10
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities	10
Analytically pricing variance swaps in commodity derivative markets under stochastic convenience yields	9
Unidirectional flocks in hydrodynamic Euler alignment system II: singular models	8
Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag	7
Wavenumber-explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers	7
Global well-posedness of the stochastic Camassa–Holm equation	7
Complete monotonicity-preserving numerical methods for time fractional ODEs	6
Nonlocal approaches for multilane traffic models	6
Numerical approximations and error analysis of the Cahn–Hilliard equation with dynamic boundary conditions	6
Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case	6
Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems	5
Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions	5
On the continuous time limit of ensemble square root filters	5
On entropic solutions to conservation laws coupled with moving bottlenecks	5
Wave breaking for a model equation for shallow water waves of moderate amplitude	5
Global smooth solutions to the 3D non-resistive MHD equations with low regularity axisymmetric data	5
A second-order accurate, energy stable numerical scheme for the one-dimensional porous medium equation by an energetic variational approach	5
Efficient numerical scheme for the anisotropic modified phase-field crystal model with a strong nonlinear vacancy potential	5
Local wellposedness of quasilinear Maxwell equations with conservative interface conditions	5

A sharp critical threshold for a traffic flow model with look-ahead dynamics	5
A fully well-balanced scheme for shallow water equations with Coriolis force	5
Kinetic and hydrodynamic models for the relativistic Cucker–Smale ensemble and emergent behaviors	5
High energy blowup and blowup time for a class of semilinear parabolic equations with singular potential on manifolds with conical singularities	5
A fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations	4
Mass-energy threshold dynamics for dipolar quantum gases	4
Strong solutions to a modified Michelson-Sivashinsky equation	4
Emergence of stochastic flocking for the discrete Cucker–Smale model with randomly switching topologies	4
On variational principles for polarization responses in electromechanical systems	4
An efficient data-driven solver for Fokker–Planck equations: algorithm and analysis	4
An ellipsoidal statistical model for a monoatomic and a polyatomic gas mixture	4
Universal approximation of symmetric and anti-symmetric functions	4
Global dynamics below the ground states for NLS under partial harmonic confinement	4
Fast Sinkhorn I: An $O(N)$ algorithm for the Wasserstein-1 metric	4
A Fourier collocation method for Schrödinger–Poisson system with perfectly matched layer	4
Degenerate Cahn–Hilliard and incompressible limit of a Keller–Segel model	4
Energy stability of variable-step L1-type schemes for time-fractional Cahn–Hilliard model	4
Complexity of randomized algorithms for underdamped Langevin dynamics	3
Microscopic and macroscopic traffic flow models including random accidents	3
Local error of a splitting scheme for a nonlinear Schrödinger-type equation with random dispersion	3
On dissipative solutions to a simplified hyperbolic Ericksen–Leslie system of liquid crystals	3
An MBO scheme for clustering and semi-supervised clustering of signed networks	3
Error analysis of Galerkin spectral methods for nonlinear optimal control problems with integral control constraint	3
Propagator norm and sharp decay estimates for Fokker–Planck equations with linear drift	3
An improved small data theorem for the Vlasov–Poisson system	3
Galerkin spectral methods for an elliptic optimal control problem with $L^2$-norm state constraint	3
Analysis of a cross-diffusion model for rival gangs interaction in a city	3
A generalized mean-field game model for the dynamics of pedestrians with limited predictive abilities	3
Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate	3
A regularity criterion for the Navier–Stokes equations via one diagonal entry of the velocity gradient	3
A general framework for nonlocal Neumann problems	3
Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations	3
The Fourier Discrepancy Function	3
Hypocoercivity of stochastic Galerkin formulations for stabilization of kinetic equations	3
On homogenization of the Landau–Lifshitz equation with rapidly oscillating material coefficient	3
ST-SVD factorization and s-diagonal tensors	3
Interaction of the elementary waves for shallow water equations with discontinuous topography	2
Lake equations with an evanescent or emergent island	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
Blowup for $C^1$ solutions of compressible Euler equations with time-dependent damping	2
The Cauchy problem for a non strictly hyperbolic $3 \times 3$ system of conservation laws arising in polymer flooding	2
Existence, regularity and weak-strong uniqueness for three-dimensional Peterlin viscoelastic model	2
Selection and mutation in a shifting and fluctuating environment	2
Kinetic model for myxobacteria with directional diffusion	2
Analysis of the role of convection in a system describing the tumor-induced angiogenesis	2
Convergence analysis of structure-preserving numerical methods based on Slotboom transformation for the Poisson–Nernst–Planck equations	2
Radon measure solutions for steady hypersonic-limit Euler flows passing two-dimensional finite non-symmetric obstacles and interactions of free concentration layers	2
Continuum limits for adaptive network dynamics	2
An energy stable finite difference scheme for the Ericksen–Leslie system with penalty function and its optimal rate convergence analysis	2

Dual quaternion matrices in multi-agent formation control	2
Tensor PDE model of biological network formation	2
The existence of compressible subsonic impinging jet flow in an arbitrary nozzle	2
Global solutions of 3D tropical climate model with finite energy	2
Cucker–Smale flocking under hierarchical leadership with time-delay and a free-will leader	2
A low Mach two-speed relaxation scheme for the compressible Euler equations with gravity	2
Decoherence rhapsody in the photosynthesis process	2
Consistency analysis of bilevel data-driven learning in inverse problems	2
The Bramson correction for integro-differential Fisher–KPP equations	2
Stability of equilibria to the model for non-isothermal electrokinetics	2
Traveling waves in a Keller–Segel model with logistic growth	2
Numerical evidence of exponential mixing by alternating shear flows	2
A quantitative version of the transversality theorem	1
Rarefied gas dynamics with external fields under specular reflection boundary condition	1
Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case	1
On the sedimentation of a droplet in Stokes flow	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
A second-order well-balanced Lagrange-projection numerical scheme for shallow water Exner equations in 1D and 2D	1
Global existence for quasilinear degenerate two-species chemotaxis system with small initial data	1
On uniform second-order nonlocal approximations to diffusion and subdiffusion equations with nonlocal effect parameter	1
Global regularity and time decay for the 2D magneto-micropolar system with fractional dissipation and partial magnetic diffusion	1
Optimal large time behavior of the compressible bipolar Navier–Stokes–Poisson system	1
The nonlinear Schrödinger equation with white noise dispersion on quantum graphs	1
On two-dimensional steady hypersonic-limit Euler flows passing ramps and radon measure solutions of compressible Euler equations	1
Asymptotic behavior of solutions to the unipolar hydrodynamic model of semiconductors with time-dependent damping in bounded domain	1
Non-uniqueness of transonic shock solutions to non-isentropic Euler–Poisson system	1
Global solutions to rotating motion of isentropic flows with cylindrical symmetry	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
Sub-exponential convergence to steady-states for 1-D Euler–Poisson equations with time-dependent damping	1
Fokker–Planck modeling of many-agent systems in swarm manufacturing: asymptotic analysis and numerical results	1
Stability of degenerate stationary solution to the outflow problem for full Navier–Stokes equations	1
Second-order accurate Dirichlet boundary conditions for linear nonlocal diffusion problems	1
Large time behavior for a Hamilton–Jacobi equation in a critical coagulation-fragmentation model	1
A variational approach for price formation models in one dimension	1
Global mild solutions of the non-cutoff Vlasov–Poisson–Boltzmann system	1
Existence and uniqueness for a stationary hybrid quantum hydrodynamical model with general pressure functional	1
Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme	1
An optimal design of random surfaces in solar cells via mini-batch stochastic gradient approach	1
On the properties of affine solutions of cold plasma equations	1
Van der Waals interactions between two hydrogen atoms: The next orders	1
Relative entropy in diffusive relaxation for a class of discrete velocities BGK models	1
Long term spatial homogeneity for a chemotaxis model with local sensing and consumption	1
Location of concentrated vortices in planar steady Euler flows	1
Reaction-diffusion equations derived from kinetic models and their Turing instability	1
Asymptotic behavior of solutions to the outflow problem for the compressible Navier–Stokes–Maxwell equations	1
A Cahn-Hilliard model coupled to viscoelasticity with large deformations	1
Numerical methods for stochastic differential equations based on Gaussian mixture	1
Invariant domain preserving central schemes for nonlinear hyperbolic systems	1
Global strong solutions for planar full compressible Hall-MHD equations with large initial data	1
Error estimate of the nonuniform $L1$ type formula for the time fractional diffusion-wave equation	1
Time-periodic solution for an incompressible magnetohydrodynamic system with an external force in $\mathbb{R}^N$	1
A nonlocal model of elliptic equation with jump coefficients on manifold	1
Global convergence of triangularized orthogonalization-free method	1
Energy conservation for 2D Euler with vorticity in $L (\operatorname{log} L)^\alpha$	1
On global regularity for a model of the regularized Boussinesq equations with zero diffusion	1
The Cahn-Hilliard-Boussinesq system with singular potential	1
Energy method for the Boltzmann equation of monatomic gaseous mixtures	1
A finite element method for Dirichlet boundary control of elliptic partial differential equations	1
Stabilized exponential time differencing schemes for the convective Allen–Cahn equation	1
Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimension	1
Existence of polynomial attractor for a class of extensible beams with nonlocal weak damping	1
Optimal sample complexity of subgradient descent for amplitude flow via non-Lipschitz matrix concentration	1
A note on optimization formulations of Markov decision processes	1
Sobolev training for physics-informed neural networks	1
Exponential synchronization of Kuramoto oscillators with time delayed coupling	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
Stability of the planar rarefaction wave to three-dimensional compressible model of viscous ions motion	1
On the convergence of frozen Gaussian approximation for linear non-strictly hyperbolic systems	1
Limiting behaviors of high dimensional stochastic spin ensembles	1
Recovery of a distributed order fractional derivative in an unknown medium	1
Design of a mode converter using thin resonant ligaments	1
Regularized least square kernel regression for streaming data	1
Some models for the interaction of long and short waves in dispersive media. Part II: Well-posedness	1
Long time existence of the Boussinesq equation with large initial data in $\mathbb{R}^n$	1
$L^\infty$ continuation principle for two-dimensional compressible nematic liquid crystal flows	1
Global well-posedness and decay of the low-regularity solution to the 3D density-dependent magnetohydrodynamic equations with vacuum	1

A Cahn–Hilliard model with a proliferation term for the proliferative-to-invasive transition of hypoxic glioma cells	1
Heterogeneous multiscale methods for rough-wall laminar viscous flow	1
Interior eigensolver for sparse Hermitian definite matrices based on Zolotarev’s functions	1
Initial mixed-boundary value problem for anisotropic fractional degenerate parabolic equations	1