Related papers: A Second-Order Nonlocal Approximation for Manifold…
Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…
In this paper, we investigate the well-posedness theory for the MHD boundary layer system in two-dimensional space. The boundary layer equations are governed by the Prandtl type equations that are derived from the full incompressible MHD…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…
We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite difference approximations, which provide a strong form of…
We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal…
Point-to-point reflection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equations. We develop a non-local,…
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…
In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and…
We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the…
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…
We show local well-posedness for the Mullins-Sekerka system with ninety degree angle boundary contact. We will describe the motion of the moving interface by a height function over a fixed reference surface. Using the theory of maximal…
We consider a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, posed on a bounded domain of R^N (N $\in$ N *), assumed to be an unknown perturbation of a reference domain. We are interested…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
In this work we develop some automatic procedures for computing high order polynomial expansions of local (un)stable manifolds for equilibria of differential equations. Our method incorporates validated truncation error bounds, and…
We present a generalization of Dirac constraint theory based on the theory of Poisson-Dirac submanifolds. The theory is formulated in a coordinate-free manner while simultaneously relaxing the invertibility condition as seen in standard…
Nonlinear extension of the integral part of a standard proportional-integral-derivative (PID) feedback control is proposed for perturbed second-order systems. The approach is model-free and requires solely the Lipschitz boundedness of the…
The local well-posedness problem is considered for the Dirac-Klein-Gordon system in two space dimensions for data in Fourier-Lebesgue spaces $\hat{H}^{s,r}$ , where $\|f\|_{\hat{H}^{s,r}} = \| \langle \xi \rangle^s \hat{f}\|_{L^{r'}}$ and…
The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…