We prove that the generalized Benjamin-Ono equations ∂tu + H∂2 xu ± u ∂xu = 0, k ≥ 4 are locally well-posed in the scaling invariant spaces Ḣsk(R) where sk = 1/2 − 1/k. Our results also hold in the nonhomogeneous spaces Hsk(R). In the case k = 3, local well-posedness is obtained in Hs(R), s > 1/3.

In this paper, adaptive discrete-time low-gain integral control strategies are presented for tracking constant reference signals for infinite-dimensional discrete-time power-stable linear systems. The discrete-time results are applied in the development of adaptive sampled-data low-gain integral control of well-posed infinite-dimensional exponentially stable linear systems. Our results consider...

The paper studies a class of conservation law models for traffic flow on a family of roads, near a junction. A Riemann Solver is constructed, where the incoming and outgoing fluxes depend Hölder continuously on the traffic density and on the drivers’ turning preferences. However, various examples show that, if junction conditions are assigned in terms of Riemann Solvers, then the Cauchy problem...

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.

We prove global well-posedness for the radial defocusing cubic wave equation

Anisotropic diffusion methods are well-known to give good qualitative results for image denoising. This paper gives a review of the anisotropic diffusion methodology and its application to image denoising. We propose a fixed-point iteration using a multigrid solver to solve a regularized anisotropic diffusion equation, which is not only well-posed, but also has a nontrivial steady-state solutio...

We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a new technique to compute the quantity of interest for any initial value, and with any given precision. Rather than focusing on a particular model for risk proc...

A crucial problem concerning Tikhonov regularization is the proper choice of the regularization parameter. This paper deals with a generalization of a parameter choice rule due to Regińska (1996) [31], analyzed and algorithmically realized through a fast fixed-point method in Bazán (2008) [3], which results in a fixed-point method for multi-parameter Tikhonov regularization called MFP. Like the...

In this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy M-complete metric spaces. We also give an affirmative partial answer to a question posed by Wardowski [D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Set Syst., {bf 222}(2013), 108-114].Some examples are also g...

‎In this paper‎, ‎we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian‎ ‎dynamic equation on time scales‎. ‎We prove the existence at least three positive solutions of the boundary‎ ‎value problem by using the Avery and Peterson fixed point theorem‎. ‎The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly‎. ‎Our results ...