Related papers: Banach fixed point and flow approach for rough ana…
In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually…
This work develops moment bounds for the controlled rough path norm of the solution of semilinear rough partial differential equations.~The novel aspects are two-fold: first we consider rough paths of low time regularity…
We describe a new approach to the problem of constructing gluing parameterizations for open neighborhoods of boundary points of moduli spaces of anti-self-dual connections over closed four-dimensional manifolds. Our approach employs general…
Leveraging techniques from the literature on geometric numerical integration, we propose a new general method to compute exact expressions for the BCH formula. In its utmost generality, the method consists in embedding the Lie algebra of…
In this paper we analyze Nitsche's method for the stationary Boussinesq system with Navier's slip and a nonlinear boundary condition. Our analysis of the formulation establishes the robustness of a finite elements scheme in arbitrarily…
We study a Boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re-enter. On this boundary part, we consider a do-nothing condition for the fluid flow, and a new artificial condition for the heat…
A new fixed point principle for complete ordered families of equivalences (COFEs) is presented, which is stronger than the standard Banach-type fixed point principle.
We prove existence and uniqueness results for (mild) solutions to some non-linear parabolic evolution equations with a rough forcing term. Our method of proof relies on a careful exploitation of the interplay between the spatial and time…
We propose a new mathematical model of groundwater flow in porous medium layered over inclined impermeable bed. In its full generality, this is a free-surface problem. To obtain analytically tractable model, we use generalized…
Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform…
By means of fixed point index theory for multi-valued maps, we provide an analogue of the classical Birkhoff--Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general…
In this paper we give sharp extension results for convoluted solutions of abstract Cauchy problems in Banach spaces. The main technique is the use of algebraic structure (for usual convolution product $\ast$) of these solutions which are…
We reprove the $\lambda$-Lemma for finite dimensional gradient flows by generalizing the well-known contraction method proof of the local (un)stable manifold theorem. This only relies on the forward Cauchy problem. We obtain a rather…
We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a…
In this article we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As…
We consider bifurcation of solutions from a given trivial branch for a class of strongly indefinite elliptic systems via the spectral flow. Our main results establish bifurcation invariants that can be obtained from the coefficients of the…
We propose a mathematical model for fluids in multiphase flows in order to establish a solid theoretical foundation for the study of their complex topology, large geometric deformations, and topological changes such as merging. Our modeling…
In this paper we consider rough differential equations on a smooth manifold $\left( M\right) .$ The main result of this paper gives sufficient conditions on the driving vector-fields so that the rough ODE's have global (in time) solutions.…
Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_{\Phi}$ with gauge $\phi$. Let $f$ be…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…