相关论文: A robust DPG method for large domains

To address the power system hardening problem, traditional approaches often adopt robust optimization (RO) that considers a fixed set of concerned contingencies, regardless of the fact that hardening some components actually renders…

The aim of this work is to establish the well-posedness of fully nonlinear partial differential equations (PDE) posed on a star-shaped network, having nonlinear Kirchhoff's boundary condition at the vertex, and possibly degenerate. We…

We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with respect to domain perturbations. This depends on the exponent…

This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled…

The theory of polar forms of polynomials is used to provide for sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the length of the largest possible real interval (parabolic stability radius), to be…

Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential boundary conditions. The widely adopted penalty-type methods,…

In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist…

We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…

We introduce a Nitsche's method for the numerical approximation of the Kirchhoff-Love plate equation under general Robin-type boundary conditions. We analyze the method by presenting a priori and a posteriori error estimates in…

We establish global stability for a chemotaxis-growth model with logarithmic sensitivity under dynamic Dirichlet boundary conditions on a 1D domain. We analyze both parabolic-parabolic and parabolic-hyperbolic systems. The key challenge is…

In the plane, we consider the problem of reconstructing a domain from the normal derivative of its Green's function (with fixed pole) relative to the Dirichlet problem for the Laplace operator. By means of the theory of conformal mappings,…

We study in this paper the well-posedness and stability for two linear Schr\"odinger equations in $d$-dimensional open bounded domain under Dirichlet boundary conditions with an infinite memory. First, we establish the well-posedness in the…

The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity $\epsilon$ of one of the two solution…

We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters are unknown as well as the distribution and moments of innoovations. The distribution of outliers $\Pi$ is…

We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…

We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…

In this article, we study the stability of solutions to a nonlinear viscoelastic plate problem with frictional damping of a memory on a part of the boundary, and a logarithmic source in a bounded domain $\Omega \subset \mathbb{R}^2.$ In…

With a small parameter $\epsilon$, Poisson-Nernst-Planck (PNP) systems over a finite one-dimensional (1D) spatial domain have steady state solutions, called 1D boundary layer solutions, which profiles form boundary layers near boundary…

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…

Methods for modeling large driven dissipative quantum systems are becoming increasingly urgent due to recent experimental progress in a number of photonic platforms. We demonstrate the positive-P method to be ideal for this purpose across a…