The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of α-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations of α-well...

We study the problem of making interpersonal well-being comparisons when individuals have heterogeneous preferences. present a robust, but incomplete, criterion for that states one individual is better off than another if intersection between extended upper contour set better-off and lower worse-off empty. implement in consumption-health space using an online survey 2260 respondents United Stat...

In this paper we propose a jump-diffusion Libor model with jumps in a high-dimensional space (Rm) and test a stable non-parametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes the deviation from the Libor market model. In practice, the procedure is FFT based, thus fast, easy to...

WELL-POSEDNESS PROPERTIES IN VARIATIONAL ANALYSIS AND ITSAPPLICATIONSbyWEI OUYANGAugust 2015Advisor: Prof. Boris S. MordukhovichMajor: Mathematics (Applied)Degree: Doctor of PhilosophyThis dissertation focuses on the study and applications of some significant properties inwell-posedness and sensitivity analysis, among which the notions of uniform metric r...

Deconvolution is usually regarded as one of the so called ill-posed problems of applied mathematics if no constraints on the unknowns can be assumed. In this paper, we discuss the idea of well-de ned statistical models being a counterpart of the notion of well-posedness. We show that constraints on the unknowns such as non-negativity and sparsity can help a great deal to get over the inherent i...

— Thanks to an approach inspired from Burq-Lebeau [6], we prove stochastic versions of Strichartz estimates for Schrödinger with harmonic potential. As a consequence, we show that the nonlinear Schrödinger equation with quadratic potential and any polynomial nonlinearity is almost surely locally well-posed in L(R) for any d ≥ 2. Then, we show that we can combine this result with the high-low fr...

We investigate the well-posedness for the 2D viscous shallow water equations in the theory of compressible fluid. Making use of the Fourier frequency localization and Bony paraproduct decomposition, closing to a stable equilibrium h0, we obtain the local well-posedness for general initial data u0 and the global well-posedness for small initial data u0 in certain scaling invariant Besov spaces, ...

We prove global well-posedness of the short-pulse equation with small initial data in Sobolev spaceHs for an integer s ≥ 2. Our analysis relies on local well-posedness results of Schäfer & Wayne [12], the correspondence of the short-pulse equation to the sine– Gordon equation in characteristic coordinates, and a number of conserved quantities of the short-pulse equation. We also prove local and...

A tensor-based method is proposed for the solution of partial differential equations defined on uncertain parameterized domains. It provides an accurate solution which is explicit with respect to parameters defining the shape of the domain, thus allowing efficient a posteriori probabilistic or parametric analyses. In the proposed method, a fictitious domain approach is first adopted for the ref...