In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partical viscosity. This model was originally proposed by Hou-Lei in [4]. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-...

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi 1995, 1996 for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is ...

In this paper we introduce a derivative-free, iterative method for solving nonlinear illposed problems Fx = y, where instead of y noisy data yδ with ‖y − yδ‖ ≤ δ are given and F : D(F ) ⊆ X → Y is a nonlinear operator between Hilbert spaces X and Y . This method is defined by splitting the operator F into a linear part A and a nonlinear part G, such that F = A + G. Then iterations are organized...

The aim of this paper is to investigate the global dynamics of a delayed diffusive twostrain disease model. We first study the well-posedness of the model. And then, by selecting appropriate Lyapunov functionals, we demonstrate that the global stability of the model is fully determined by the basic reproduction number. Furthermore, using Schauder fixed point theorem and constructing a pair of u...

The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of conditional reciprocal continuity. We demonstrate that conditional reciprocal continuity ensures the existence of fixed points under contractive conditions which otherwise do not ensure the existence of fixed points. Our results generalize and extend several well-known fixed poin...

This paper presents an algorithm for learning the time-varying shape of a non-rigid 3D object from uncalibrated 2D tracking data. We model shape motion as a rigid component (rotation and translation) combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed. We constrain the problem by assuming that the object shape at each time instant is drawn fr...

Ill-posed problems are numerically underdetermined. It is therefore often beneficial to impose known properties of the desired solution, such as nonnegativity, during the solution process. This paper proposes the use of an interior-point method in conjunction with truncated iteration for the solution of large-scale linear discrete ill-posed problems with box constraints. An estimate of the erro...

In a bivariate context, we consider ill-posed inverse problems with incomplete theoretical and data information. We demonstrate the use of information theoretic methods for information recovery for a range of under-identified choice problems with more unknowns than data points. © 2007 Elsevier B.V. All rights reserved.

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.