The notion of topological equivalence plays an essential role in the study dynamical systems flows. However, it is inherently difficult to generalize this concept without well-posedness sense Hadamard. In study, we formulate a “topological equivalence” between such based on axiomatic theory dynamics proposed by Yorke, and discuss its relation with usual definition. During process, Yorke's actio...

The paper is devoted to the mathematical analysis of Cauchy problem for general cross-diffusion systems without any assumption about its entropic structure. A global existence result nonnegative solutions obtained by applying a classical Schauder fixed point theorem. proof upgraded enhancing regularity solution, namely gradient belongs space Lr((0,T)×Ω) some r>2. To this aim, Schauder's strateg...

Galbrun's equation, which is a second order partial differential equation describing the evolution of so-called Lagrangian displacement vector field, can be used to study acoustics in background flows as well perturbations astrophysical flows. Our starting point for deriving linearized Euler's equations, first system equations that describe Eulerian flow perturbations. Given solution we introdu...

In the thesis, interior conductivity reconstruction problems inferring from the interior current density data are considered. It is our main result that an anisotropic conductivity reconstruction in two dimensions is well-posed. This is relevant to an application of a medical diagnosis on human organism since human organism typically has an anisotropic conductivity. In the first part of thesis,...

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems are established

In this paper, we consider distribution solutions to the aggregation equation ρt + div(ρu) = 0, u = −∇V ∗ρ in R where the density ρ concentrates on a co-dimension one manifold. We show that an evolution equation for the manifold itself completely determines the dynamics of such solutions. We refer to such solutions aggregation sheets. When the equation for the sheet is linearly well-posed, we s...

The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bound...