相关论文: Uniqueness and stability for the solution of a non…

We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…

In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant…

In this paper, we show that a geometrical condition on $2\times2$ systems of conservation laws leads to non-uniqueness in the class of 1D continuous functions. This demonstrates that the Liu Entropy Condition alone is insufficient to…

We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we study well-posedness and establish the existence of…

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem)…

The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant…

We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…

The notion of strict singular characteristics is important in the wellposedness issue of singular dynamics on the cut locus of the viscosity solutions. We provide an intuitive and rigorous proof of the existence of the strict singular…

We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give…

We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be singular at the level zero, and solutions may change sign. If…

In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to…

We establish the uniqueness of a saddle-shaped solution to the diffusion equation $-\Delta u = f(u)$ in all of $\mathbb{R}^{2m}$, where $f$ is of bistable type, in every even dimension $2m \geq 2$. In addition, we prove its stability…

We examine the minimal magnitude of perturbations necessary to change the number $N$ of static equilibrium points of a convex solid $K$. We call the normalized volume of the minimally necessary truncation robustness and we seek shapes with…

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over $\mathbb{C}$ (resp. $\mathbb{R}$), and let $\mathcal{P}$…

We investigate the point singularity of very weak solutions $(\mathbf{u},\mathbf{B})$ to the stationary MHD equations. More precisely, assume that the solution $(\mathbf{u},\mathbf{B})$ in the punctured ball $B_2\setminus \{0\}$ satisfies…

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…

Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme…

We consider the incompressible Euler equations in the half cylinder $ \mathbb{R}_{>0}\times\mathbb{T}$. In this domain, any vorticity which is independent of $x_2$ defines a stationary solution. We prove that such a stationary solution is…

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…

We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…