相关论文: Global existence for the confined Muskat problem

For 3-D quadratic quasilinear wave equations with or without null conditions in exterior domains, when the compatible initial data and Dirichlet boundary values are given, the global existence or the maximal existence time of small data…

We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic…

We prove a global existence result for weak solutions to a one-dimensional free boundary problem with flux boundary conditions describing swelling along a halfline. Additionally, we show that solutions are not only unique but also depend…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…

We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport metric which renders the solution map Lipschitz continuous…

The paper deals with initial-boundary value problems for the linear wave equation whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^2$ under small…

This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…

We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative…

We propose a new framework to design and analyze accelerated methods that solve general monotone equation (ME) problems $F(x)=0$. Traditional approaches include generalized steepest descent methods and inexact Newton-type methods. If $F$ is…

In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…

Gompf's end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$ topology, but for which the exotic differentiable structure is confined to a region which…

This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and…

This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance:…

This short note is motivated by an attempt to understand the distinction between the Laplace operator and the hyperbolic Laplacian on the unit ball of $\mathbb{R}^n$, regarding the Lipschitz continuity of the solutions to the corresponding…

This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…

The focusing cubic wave equation in three spatial dimensions has the explicit solution $\sqrt{2}/t$. We study the stability of the blowup described by this solution as $t \to 0$ without symmetry restrictions on the data. Via the conformal…

The question of finite time singularity formation vs. global existence for solutions to the generalized Constantin-Lax-Majda equation is studied, with particular emphasis on the influence of a parameter $a$ which controls the strength of…

We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of $p$-type, $p \geq 2$. The main novelty is the use of a linearization technique going back to [28] in order to interpret…

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t),…