There exist several papers about boundary value problems with impulŽ sive effects at fixed points, but the different techniques employed for w x w x instance, limit arguments in 1, 3 , topological degree 10 , fixed point w x w x. theorems 9 or set-valued maps 2 do not seem applicable to problems with impulses at variable times. Ž w x. Recently, some comparison principles have appeared see 4, 8 ...

Given γ ≥ 0, let us consider the following differential inclusion (S) ẍ(t) + γ ẋ(t) + ∂Φ(x(t)) 3 0, t ∈ R+, where Φ : Rd → R ∪ {+∞} is a lower semicontinuous convex function such that int(domΦ) 6= ∅. The operator ∂Φ denotes the subdifferential of Φ. When Φ = f + δK with f : Rd → R a smooth convex function and K ⊂ Rd a closed convex set, inclusion (S) describes the motion of a discrete mechanica...

We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by consideri...

In dynamical systems with divided phase space, the vicinity of the boundary between regular and chaotic regions is often “sticky,” that is, trapping orbits from the chaotic region for long times. Here, we investigate the stickiness in the simplest mushroom billiard, which has a smooth such boundary, but surprisingly subtle behaviour. As a measure of stickiness, we investigate P (t), the probabi...

in this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. the conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. this study evaluates the advantages of using the integral form of the equations in the...

In the analysis of narrow escape problems in Sect. 7.2, we assumed that the holes in the boundary of the domain were always open. However, if we view each pore as a stochastically gated ion channel, for example, then one has the problem of analyzing the diffusion equation in a domain with a randomly switching boundary (or partial boundary). Such a scenario also arises in the case of membrane di...

Contents 1 Introduction 2 2 The Dirichlet problem and the boundary trace 7 2. Abstract We study the boundary value problem with measures for (E1) −∆u + g(|∇u|) = 0 in a bounded domain Ω in R N , satisfying (E2) u = µ on ∂Ω and prove that if g ∈ L 1 (1, ∞; t −(2N +1)/N dt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r) ≥ r q with q > 1 we prove that any pos...

where ∂i = ∂/∂x i and D = ∪ 0≤t≤T {t}×Dt, Dt ⊂ R. Here V k = δvi = vk and we use the summation convention over repeated upper and lower indices. The velocity vector field of the fluid is V , p is the pressure and Dt is the domain the fluid occupies at time t. We also require boundary conditions on the free boundary ∂D; p = 0, on ∂D, (1.3) (∂t + V ∂k)|∂D ∈ T (∂D), (1.4) Condition (1.3) says that...