In this paper we study several existing notions of well-posedness for vector optimization problems. We distinguish them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are ...

We prove global well-posedness for the cubic, defocusing, nonlinear Schrödinger equation on R2 with data u0 ∈ H s(R2), s > 1/4. We accomplish this by improving the almost Morawetz estimates in [9].

Children’s health is of great importance for their ongoing growth and development. It is therefore important to increase our knowledge and understanding of the factors that infl uence children’s health. The main areas of interest for the Swedish part of the ArctiChildren project are bullying and stress-related problems, as well as children’s experiences of health and well-being, ethical learnin...

Vickers and Wilson ([26]) have shown global hyperbolicity of the conical spacetime in the sense of well-posedness of the initial value problem for the wave equation in generalized functions. We add the aspect of metric splitting and preliminary thoughts on Cauchy hypersurfaces and causal curves. AMS Mathematics Subject Classi cation (2010): 46F30, 83C75

Positive future thinking (having things to look forward to) is an important element of well-being. Two studies tested whether the link between well-being and positive future thinking is restricted to self-related future thinking or extends to more general, script-like mental representations of the future. Well-being in a community sample (Study 1) was related to ability to think of positive fut...

This paper concerns the global structure stability of impact-generated tensile waves in a 1D bar made of a rubber-like material. Because the stress–strain curve changes from concave to convex as the strain increases, the governing quasi-linear system of partial differential equations, though hyperbolic, fails to be ‘genuinely non-linear’ so that the standard form of the initial-boundary value p...

We prove an “almost conservation law” to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in H(R) when n = 2, 3 and s > 4 7 , 5 6 , respectively.

OBJECTIVES Recently, a model of reminiscence and well-being has emerged in which reminiscence functions have been shown to predict both the mental and physical health of middle-aged and older adults. Yet this model has thus far been verified only with North American, Western European, and Australian participants. This study was undertaken to compare the latent structure of responses between Can...

We prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in H s , for s > 2/3 for small L 2 data. The result follows from an application of the " I-method ". This method allows to define a modification of the energy norm H 1 that is " almost conserved " and can be used to perform an iteration argument. We also remark that the same argument can be us...

Transport equations arise in various areas of fluid mechanics, but the precise conditions on the vector field for them to be well-posed are still not fully understood. The renormalized theory of DiPerna and Lions for linear transport equations with unsmooth coefficient uses the tools of approximation of an arbitrary weak solution by smooth functions, and the renormalization property, that is to...