In this article we focus on the global well-posedness of the differential equation utt − ∆u+ |u|k∂j(ut) = |u|p−1u in Ω× (0, T ), where ∂j is a sub-differential of a continuous convex function j. Under some conditions on j and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assu...

What happens when people suppress their emotions when they sacrifice for a romantic partner? This multimethod study investigates how suppressing emotions during sacrifice shapes affective and relationship outcomes. In Part 1, dating couples came into the laboratory to discuss important romantic relationship sacrifices. Suppressing emotions was associated with emotional costs for the partner dis...

We consider chains of particles with nearest-neighbor coupling, independently subjected to noise, all initially in the same well of a symmetric double-well potential. If there are sufficiently few particles, transitions from one well to another are “collective”; i.e., all particles remain close together as they make the passage from one well to the other. In longer chains, only a fraction of th...

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schrödinger equation is shown to be well-posed, in a relatively weak sense, in certain function spaces wider than L. Solutions are constructed as sums of infinite series of multilinear operators applied to initial data, and these multilinear operators are analyzed directly.

Multi-channel super-resolution is a means of recovering high frequency information b y trading o f f the temporal bandwidth. Almost all the methods proposed in the literature are based on optimizing a cost function. But since the problem is usually ill-posed, one needs to impose some regularity constraints. However, regularity constraints tend to attenuate high frequency contents of data (usual...

Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle for choosing regularization parameter are obtained.

In this study, we explored the relation between romantic involvement status, actual/ideal self-discrepancy, and psychological well-being. We hypothesized that romantically involved individuals would report being closer to their ideal selves than would romantically uninvolved individuals. We also hypothesized that the reduced self-discrepancy reported by romantically involved individuals would b...

Feminist psychologists have long posited that relationship authenticity (i.e., the congruence between what one thinks and feels and what one does and says in relational contexts) is integral to self-esteem and well-being. Guided by a feminist developmental framework, the authors investigated the role of relationship authenticity in promoting girls' self-esteem over the course of adolescence. La...

We consider an inverse initial value problem of the biparabolic equation; this problem is ill-posed and the regularization methods are needed to stabilize the numerical computations. This paper firstly establishes a conditional stability of Holder type, then uses a modified regularization method to overcome its ill-posedness and gives the convergence estimate under an a-priori assumption for th...

We show that the Cauchy problem for the quintic NLS on R is globally well-posed in Hs for 4/9 < s ≤ 1/2. Since we work below the energy space we can not immediately use the energy.Instead we use the “I-method” introduced by J.Colliander,M.Keel,G.Staffilani, H.Takaoka,T.Tao.This method allows us to define a modification of the energy functional that is “almost conserved” and thus can be used to ...