Communications in Mathematical Sciences

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 drift coefficients

Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case

Stability of degenerate stationary solution to the outflow problem for full Navier–Stokes equations

Galerkin spectral methods for an elliptic optimal control problem with $L^2$-norm state constraint

Existence of global weak solutions to the compressible Ericksen–Leslie system in dimension one

Complete monotonicity-preserving numerical methods for time fractional ODEs

Global solutions of 3D tropical climate model with finite energy

The existence of compressible subsonic impinging jet flow in an arbitrary nozzle

Interaction of the elementary waves for shallow water equations with discontinuous topography

Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag

Exponential synchronization of Kuramoto oscillators with time delayed coupling

Entropy admissibility of the limit solution for a nonlocal model of traffic flow

Global discontinuous solution for $1D$ isentropic gas dynamics system