We investigate a moving boundary problem with a gradient flow structure which generalizes Hele-Shaw flow driven solely by surface tension to the case of nonconstant surface tension coefficient taken along with the liquid particles at boundary. The resulting evolution problem is first order in time, contains a third-order nonlinear pseudodifferential operator and is degenerate parabolic. Well-po...

In this paper, we show that the solution of the supercrtical surface quasi-geostrophic (SQG) equation, with initial data in a critical Besov space, belongs to a subanalytic Gevrey class. In order to prove this, a suitable estimate on the nonlinear term, in the form of a commutator, is required. We express the commutator as a bilinear multiplier operator and obtain single-scale estimates for its...

A general form of the polarization matrix valid for any type of electromagnetic radiation (plane waves, multipole radiation etc.) is defined in terms of a certain bilinear form in the field-strength tensor. The quantum counterpart is determined as an operator matrix with normal-ordered elements with respect to the creation and annihilation operators. The zero-point oscillations (ZPO) of polariz...

The long time behavior and detailed convergence analysis of Langevin equations have received increased attention in recent years. Difficulties arise from a lack coercivity, usually termed hypocoercivity, the underlying kinetic Fokker–Planck operator, which is consequence partially deterministic nature second order stochastic differential equation. In this manuscript, effect controlling confinem...

The aim of this paper is to establish some a priori bounds for solutions of Landesman-Lazer problem. We show the application for the solution structure of the nonlinear diierential equation of the fourth order 1. The general theory Let X be a real Banach space with the norm k k and let D(L) X be the domain of the closed Fredholm operator L : D(L) ! X with index zero. We shall suppose that 0 is ...

In this paper, we propose two lower order nonconforming rectangular elements for the Reissner-Mindlin plate. The first one uses the conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element to approximate the displacement, whereas the second one uses the modified nonconforming rotated Q1 element to approximate both the rotation...

There has recently been much interest in approximation by linear combinations of functions taken from a redundant set 79. That is, the elements of 79 are not linearly independent. Perhaps the first example of this type was considered by Schmidt in 1907 [6] who considered the approximation of functions f ( x , y ) of two variables by bilinear forms ~-~tfl=lUi(X)Vi(y ) in L2([0,112). This problem...

In this paper, we design a novel alternating update method for solving a class of generalized bilinear programming problem, where each subproblem is regularized by a positive-definite proximal term to guarantee the convergence of the method. By using the tool of the variational inequality and the property of a monotonicity operator, its global convergence is analyzed and a worst-case O(1/t) con...

We consider the unique radially symmetric degree-one solution w(x) = U(r)e of the Ginzbug-Landau equation in R ∆w + (1− |w|)w = 0, |w(x)| → 1 as |x| → +∞. We provide an elementary proof of its locally minimizing character and non-degeneracy up to the obvious invariance of the equation, in the natural Hilbert space for its second variation bilinear form. The proof reduces to an optimal vector-va...