Some fixed point theorems and common fixed point theorem in Logarithmic convex structure areproved.

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...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

We prove that the KdV-Burgers is globally well-posed in H−1(T) with a solution-map that is analytic fromH−1(T) to C([0, T ];H−1(T)) whereas it is ill-posed in Hs(T), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(T) to even D′(T) at any fixed t > 0 small enough. In view of the result of Kappeler and Topalov for KdV it thus appears that even if the dis...

We discuss some new well-posedness results for the continuity equation in arbitrary space dimension and we then illustrate applications to a system of conservation laws in one space dimension known as the chromatography system. In the last section, we discuss some related open problems.

To assess the quality of solutions in stochastic inverse problems, a proper measure for the distance of random variables is essential. The aim of this note is the comparison of the metrics of Ky Fan and Prokhorov with other concepts such as expected values, probability estimates and almost sure convergence. In ill-posed problems one aims to find an appropriate solution x† to an equation of the ...

Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well-posedness, we discuss positivity, L∞-contractivity and further invariance properties. We show that the parabolic problem with dynamic boundary conditions enjoy these properties if an...

This paper describes a new method for tracking of a human body in 3D motion by using constraints imposed on the body from the scene. An image-based approach for tracking exclusively uses a geometrical model of the human body. Since the model usually has a large number of degrees of freedom (DOF), a chance to be corrupted by noise increases during the tracking process, and the tracking may fall ...

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.