The dynamics of an elastic bar that appears in two phases can be described by viscosity-capillarity models. They contain numerically complicated third-order or fully nonlocal terms to account for surface energies. Based on work of Solci and Vitali [20] we analyze an alternative modelling approach that does not involve third-order differential operators. It is proven that solutions of the new model tend to solutions of the classical viscosity-capillarity model provided a so-called coupling parameter tends to infinity. Numerical experiments illustrate our findings. In fact it is shown that the new model provides a reliable and efficient approach to compute approximate solutions for the classical viscosity-capillarity model.

This paper is concerned with the existence of solutions to the class of nonlocal boundary value problems of the type -M\left(\int_{\Omega}|\nabla u|^2\right)\Delta u = f(x,u), \text { in } \Omega, \ u=0, \text{ on } \partial \Omega, where \Omega is a smooth bounded domain of \mathbb{R}^N and M is a positive continuous function. By assuming that f(x, u) is a Carathéodory function which growths at most |u|^{\frac{N}{N-2}} , N \geq 3 , and under a suitable growth condition on M , one proves an existence result by applying the Leray–Schauder fixed point theorem.

In this paper, we give some regularities and limit theorems of some additive functionals of symmetric stable process of index 1<\alpha\leq2 in some anisotropic Besov spaces.

A corner is defined to be the vertex of a strict cone locally containing the support of a truss and having locally empty intersection with the support of the applied force. A topological perturbation called corner cutting is defined in two dimensions and the process is shown to have a negative effect on the mass of planar trusses, independent of the angle of the corner. Minimal, finite, planar trusses are therefore free of corners. Applied point forces are shown to be balanced by at least one truss, thereby showing that the admissible class is nonempty. Explicit mass and geometric bounds are presented as part of this construction.

This work is an attempt to develop the uniqueness theory of entropy solution for the Cauchy problem associated to a general non-isotropic nonlinear strongly degenerate parabolic-hyperbolic equation. Our aim is to extend, at the same time, results of [1] and [11]. The novelty in this paper is the fact that we are dealing with general anisotropic diffusion problems, not necessarily with Lipschitz convection-diffusion flux functions in the whole space. Moreover, the source term depends on the unknown function of the problem. Under an abstract lemma and an additional assumption, we ensure the comparison principle which leads us to the uniqueness. In unbounded domains without Lipschitz condition on the convection and diffusion flux functions, this assumption seems to be optimal to establish uniqueness (cf. [1], [3], [14]).

We define the notion of strong projective limit of Banach Lie algebroids. We study the associated structures of Fréchet bundles and the compatibility with the different morphisms. This kind of structures seems to be a convenient framework for various situations.

We consider the class of C^1 partially hyperbolic volume-preserving flows with one-dimensional central direction endowed with the C^1 -Whitney topology. We prove that, within this class, any flow can be approximated by an ergodic C^2 volume-preserving flow and so, as a consequence, ergodicity is dense.

In this paper we provide an overview of some basic topics in interest rate theory from the point of view of arbitrage free pricing. We cover short rate models, affine term structure models, inversion of the yield curve and the Musiela parameterization. We treat geometric interest rate theory in some detail, and we also review the potential approach to positive interest rates. The text is essentially self-contained, and references to the literature can be found in Section 6.

We characterize the intersection of the ranges of a class of co-analytic Toeplitz operators by considering this set as the dual space of the Privalov space N^p , 1 < p < ∞ , in a certain topology. For a fixed p we define the class H_p consisting of those de Branges spaces \mathscr{H}(b) such that the function b is not an extreme point of the unit ball of H^∞ , and the associated measure μ_b for b satisfies an additional condition. It is proved that the function f analytic on \mathbf D is a multiplier of every de Branges space from H_p if and only if f is in the intersection of the ranges of all Toeplitz operators belonging to the class H_p . We show that this is true if and only if the Taylor coefficients \hat{f}(n) of f decay like O(\exp (−cn^{1/(p + 1)})) for a positive constant c .

In this paper we study the asymptotic stability of the trivial solution of third order nonlinear delay differential equations of the form x'''(t) + f(x(t), x'(t))x''(t) + g(x(t − r), x'(t − r)) + h(x(t − r)) = 0, where r > 0 is a constant delay. In proving our result we make use of Lyapunov’s second method by constructing a Lyapunov functional.