Related papers: A stability result for Neumann problems in dimensi…
We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm stabilization, obtained by penalizing the residual measured…
We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. Since 2010 an interior a priori $L^\infty$ bound for stable solutions is known to hold in dimensions $n \leq 4$…
The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions $n\geq3$ is completely open. In…
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schr\"odinger equations in dimensions $n \geq 3$, for solutions which have large, but finite, energy and large, but finite,…
Decompositions of the world into systems have typically been regarded as arbitrary extra-theoretical assumptions in discussions of quantum measurement. One can instead regard decompositions as part of the theory, and ask what conditions…
This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schr\"odinger equations with subcritical exponent. For some smooth bounded domain $\Omega\subset \mathbf R^n$, our boundary condition is given…
Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the…
The purpose of this paper is to study the stability of some unilateral free-discontinuity problems, under perturbations of the discontinuity sets in the Hausdorff metric.
It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincar\'e operator on the boundary of the domain or its inversion in a sphere has at least one negative eigenvalue. The…
Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish $W^{1,\infty}$ regularity for its solutions. Combined with a uniform $L^6$ estimate, such regularity leads to the validity…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow from an abstract lemma stating that it is…
It is known that spatial curvature can stabilize extra dimensions in Lovelock gravity. In the present paper we study stability of the stabilization solutions in 3-d order Lovelock gravity. We show that in the case of negative spatial…
Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases,…
We address a stability threshold problem of the Couette flow $(y,0,0)$ in a uniform magnetic fleld $\alpha(\sigma,0,1)$ with $\sigma\in\mathbb{Q}$ for the 3D MHD equations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. Previously, the…
We prove that flat ground state solutions ($i.e.$ minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the…