We study the problem of existence of weak right or left or strong coprime factorizations in H-infinity over the right half-plane of an analytic function defined in some subset of the right half-plane. We give necessary and sufficient conditions for the existence of such coprime factorizations in terms of an optimal control problem over the doubly infinite continuous-time axis. In particular, we...

Modern modeling tools often give descriptor or DAE models, i.e., models consisting of a mixture of differential and algebraic relationships. The introduction of stochastic signals into such models in connection with filtering problems raises several questions of well-posedness. The main problem is that the system equations may contain hidden relationships affecting variables defined as white no...

We complete the known results on the Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in H−1(R) with a solution-map that is analytic from H−1(R) to C([0, T ];H−1(R)) whereas it is ill-posed in Hs(R), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(R) to even D′(R) at any fixed t > 0 small enough....

In this paper we study local well-posedness in the energy space for a family of dispersive equations that can be seen as dispersive " interpolations " between the KdV and the Benjamin-Ono equation.

background: understanding customers has become an urgent topic for increasing competitiveness. the purpopse of  the study was to develop a qualitative dynamic attribute value model which provides insight into the customers' value for healthcare institute managers by conducting the initial open-ended questionnaire survey to select participants purposefully. methods: a total number of 427 questio...

In this article, we establish new results about the ill-posedness of the Cauchy problem for the modified Korteweg-de Vries and the defocusing modified Korteweg-de Vries equations, in the periodic case. The lack of local well-posedness is in the sense that the dependence of solutions upon initial data fails to be continuous. We also develop a method for obtaining ill-posedness results in the per...

In this paper we study some properties of the classical Arnoldi based methods for solving infinite dimensional linear equations involving compact operators. These problems are intrinsically ill-posed since a compact operator does not admit a bounded inverse. We study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator.

In this paper we propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly non resonant dispersive equations. As an example we obtain unconditional well-posedness of the Cauchy problem below H for a large class of one-dimensional dispersive equations with a dispersion that is greater or equal to the one of the Benjamin-Ono equation. Since this is do...

We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae...

We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed (cf. [15]). In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo...