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  • Alsedà–Misiurewicz systems with place-dependent probabilities
    Nonlinearity (IF 1.505) Pub Date : 2020-10-11
    Klaudiusz Czudek

    We consider systems of two specific piecewise linear homeomorphisms of the unit interval, so called Alsedà–Misiurewicz systems, and investigate the basic properties of Markov chains which arise when these two transformations are applied randomly with probabilities depending on the point of the interval. Though this iterated function system is not contracting in average and known methods do not apply

    更新日期:2020-10-12
  • Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification
    Nonlinearity (IF 1.505) Pub Date : 2020-10-11
    Ji-hua Ma and Yan-fang Zhang

    We calculate topological Hausdorff dimensions of a class of fractal squares by constructing certain self-similar curves. Examples include some generalized Sierpiński carpets, which have the same Hausdorff dimensions but different topological Hausdorff dimensions. Applications are given to the study of Lipschitz equivalence of fractal squares.

    更新日期:2020-10-12
  • Non-regular g -measures and variable length memory chains
    Nonlinearity (IF 1.505) Pub Date : 2020-10-08
    Ricardo F Ferreira, Sandro Gallo and Frédéric Paccaut

    It is well-known that there always exists at least one stationary measure compatible with a continuous g -function g . Here we prove that if the set of discontinuities of a g -function g has null measure under a candidate measure obtained by some asymptotic procedure, then this candidate measure is compatible with g . We explore several implications of this result, and discuss comparisons with the

    更新日期:2020-10-12
  • Fourier approximation of the statistical properties of Anosov maps on tori
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Harry Crimmins and Gary Froyland

    We study the stability of statistical properties of Anosov maps on tori by examining the stability of the spectrum of an analytically twisted Perron–Frobenius operator on the anisotropic Banach spaces of Gouëzel and Liverani (2006 Ergod. Theor. Dyn. Syst. 26 189–217). By extending our previous work in Crimmins and Froyland (2019 Ann. Henri Poincaré 20 3113–3161), we obtain the stability of various

    更新日期:2020-10-08
  • Nonlinear perturbations of evolution systems in scales of Banach spaces
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Martin Friesen and Oleksandr Kutoviy

    A variant of the abstract Cauchy–Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6134/nonab9dc9ieqn1.gif] {$\frac{\mathrm{d}u\left(t\right)}{\mathrm{d}t}=A\left(t\right)u\left(t\right)+B\left(u\left(t\right),t\right),\enspace u\left(0\right)=x$} in a

    更新日期:2020-10-08
  • Computability at zero temperature
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Michael Burr and Christian Wolf

    We investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an upper semi-computable function on the space of continuous potentials, but it is not computable. Next, we consider locally constant potentials for which the zero-temperature measure

    更新日期:2020-10-08
  • On the smallness condition in linear inviscid damping: monotonicity and resonance chains
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Yu Deng and Christian Zillinger

    We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6176/nonaba236ieqn1.gif] {${\mathbb{T}}_{L}{\times}\mathbb{R}$} . Here, we construct a model which is closely related to a small high frequency perturbation around Couette flow, which exhibits linear inviscid damping for L sufficiently small, but

    更新日期:2020-10-08
  • Completely degenerate responsive tori in Hamiltonian systems
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Wen Si and Yingfei Yi

    We consider the existence of responsive tori for the completely degenerate Hamiltonian system with the following Hamiltonian ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6072/nonaba093ieqn1.gif] {$H\left(\theta ,I,x,y,{\epsilon}\right)=\langle \omega ,I\rangle +\lambda \frac{{x}^{n}}{n}+\frac{{y}^{m}}{m}+{\epsilon}P\left(\theta ,x,y,{\epsilon}\right),\enspace \left(\theta ,I,x,y\right)\in {\m

    更新日期:2020-10-08
  • Numerical simulations for the energy-supercritical nonlinear wave equation
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Jason Murphy and Yanzhi Zhang

    We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numerically that the critical Sobolev norm of solutions remains bounded in time. This lends support to conditional scattering results that have been recently established for nonlinear wave equations.

    更新日期:2020-10-08
  • Global existence and blow-up of solutions to a nonlocal Kirchhoff diffusion problem
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Hang Ding and Jun Zhou

    In this paper, we revisit the following nonlocal Kirchhoff diffusion problem:∂tu+M([u]s2)LKu=|u|p−2u,inΩ×R+,u(x,t)=0,in(RN\Ω)×R+,u(x,0)=u0(x),inΩ,where ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn2.gif] {${\Omega}\subset {\mathbb{R}}^{N}$} is a bounded domain with Lipschitz boundary, [ u ] s is the Gagliardo seminorm of u , 0 < s < min{1, N /2}, ##IMG## [http://ej.iop.org/i

    更新日期:2020-10-08
  • Energy asymptotics of a Dirichlet to Neumann problem related to water waves
    Nonlinearity (IF 1.505) Pub Date : 2020-10-06
    Pietro Miraglio and Enrico Valdinoci

    We consider a Dirichlet to Neumann operator ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5997/nonab9dcbieqn1.gif] {${\mathcal{L}}_{a}$} arising in a model for water waves, with a nonlocal parameter a ∈ (−1, 1). We deduce the expression of the operator in terms of the Fourier transform, highlighting a local behaviour for small frequencies and a nonlocal behaviour for large frequencies. We further

    更新日期:2020-10-07
  • On the directional derivative of the Hausdorff dimension of quadratic polynomial Julia sets at 1/4
    Nonlinearity (IF 1.505) Pub Date : 2020-10-06
    Ludwik Jaksztas

    Let d ( ɛ ) and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5919/nonab9a1aieqn1.gif] {$\mathcal{D}\left(\delta \right)$} denote the Hausdorff dimension of the Julia sets of the polynomials p ɛ ( z ) = z 2 + 1/4 + ɛ and f δ ( z ) = (1 + δ ) z + z 2 respectively. In this paper we will study the directional derivative of the functions d ( ɛ ) and ##IMG## [http://ej.iop.org/images/0951-7715/33/1

    更新日期:2020-10-07
  • Linear relations for Laurent polynomials and lattice equations
    Nonlinearity (IF 1.505) Pub Date : 2020-10-06
    Andrew N W Hone and Joe Pallister

    A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. Recurrences with this property appear in diverse areas of mathematics and physics, ranging from Lie theory and supersymmetric gauge theories to Teichmüller theory and dimer models. In many cases where such recurrences appear, there is a common structural

    更新日期:2020-10-07
  • Synchronization of Kuramoto oscillators in dense networks
    Nonlinearity (IF 1.505) Pub Date : 2020-10-04
    Jianfeng Lu and Stefan Steinerberger

    We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let G = ( V , E ) be a connected graph and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5905/nonab9baaieqn1.gif] {${\left({a}_{ij}\right)}_{i,j=1}^{n}$} denotes its adjacency matrix. Let the function

    更新日期:2020-10-05
  • Crossing periodic orbits of nonsmooth Liénard systems and applications
    Nonlinearity (IF 1.505) Pub Date : 2020-10-04
    Tao Li, Hebai Chen and Xingwu Chen

    Continuing the investigation for the number of crossing periodic orbits of nonsmooth Liénard systems in (2008 Nonlinearity 21 2121–42) for the case of a unique equilibrium, in this paper we allow the considered system to have one or multiple equilibria. By constructing two control functions that are decreasing in a much narrower interval than the one used in the above work in the estimate of divergence

    更新日期:2020-10-05
  • Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks
    Nonlinearity (IF 1.505) Pub Date : 2020-10-04
    Tommaso Lorenzi and Camille Pouchol

    We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual populations whose phenotypic fitness landscape is characterised by multiple peaks. First we consider the case where phenotypic changes do not occur, and then we include the effect of heritable phenotypic changes. In the former case the model is formulated as an integrodifferential equation

    更新日期:2020-10-05
  • On omega limiting sets of infinite dimensional Volterra operators
    Nonlinearity (IF 1.505) Pub Date : 2020-09-30
    Farrukh Mukhamedov, Otabek Khakimov and Ahmad Fadillah Embong

    In the present paper, we are aiming to study limiting behaviour of infinite dimensional Volterra operators. We introduce two classes ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5875/nonab9a1cieqn1.gif] {${\tilde {\mathcal{V}}}^{+}$} and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5875/nonab9a1cieqn2.gif] {${\tilde {\mathcal{V}}}^{-}$} of infinite dimensional Volterra operators. For operators

    更新日期:2020-10-02
  • Large deviations for denominators of continued fractions
    Nonlinearity (IF 1.505) Pub Date : 2020-09-30
    Hiroki Takahasi

    We give exponential upper bounds on the probability with which the denominator of the n th convergent in the regular continued fraction expansion stays away from the mean ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5861/nonab9a1dieqn1.gif] {$\frac{n{\pi }^{2}}{12\enspace \mathrm{log}\enspace 2}$} . The exponential rate is best possible, given by an analytic function related to the dimension spectrum

    更新日期:2020-10-02
  • Dynamics of a chemostat with periodic nutrient supply and delay in the growth
    Nonlinearity (IF 1.505) Pub Date : 2020-09-30
    Pablo Amster, Gonzalo Robledo and Daniel Sepúlveda

    This paper introduces a new consideration in the well known chemostat model of a one-species with a periodic input of single nutrient with period ω , which is described by a system of differential delay equations. The delay represents the interval time between the consumption of nutrient and its metabolization by the microbial species. We obtain a necessary and sufficient condition ensuring the existence

    更新日期:2020-10-02
  • A proof of unlimited multistability for phosphorylation cycles
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Elisenda Feliu, Alan D Rendall and Carsten Wiuf

    The multiple futile cycle is a phosphorylation system in which a molecular substrate might be phosphorylated sequentially n times by means of an enzymatic mechanism. The system has been studied mathematically using reaction network theory and ordinary differential equations. It is known that the system might have at least as many as ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5629/nonab9a1eieqn1

    更新日期:2020-09-30
  • Schmidt’s game and nonuniformly expanding interval maps
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Jason Duvall

    We study a class of nonuniformly expanding interval maps with a neutral fixed point at 0, a class that includes Manneville–Pomeau maps. We prove that the set of points whose forward orbits miss an interval with left endpoint 0 is strong winning for Schmidt’s game. Strong winning sets are dense, have full Hausdorff dimension, and satisfy a countable intersection property. Similar results were known

    更新日期:2020-09-30
  • Variance reduction for effective energies of random lattices in the Thomas–Fermi–von Weizsäcker model
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Julian Fischer and Michael Kniely

    In the computation of the material properties of random alloys, the method of ‘special quasirandom structures’ attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in

    更新日期:2020-09-30
  • Micropolar meets Newtonian in 3D. The Rayleigh–Bénard problem for large Prandtl numbers
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Piotr Kalita and Grzegorz Łukaszewicz

    We consider the Rayleigh–Bénard problem for the three-dimensional Boussinesq system for the micropolar fluid. We introduce the notion of the multivalued eventual semiflow and prove the existence of the two-space global attractor ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5686/nonab9729ieqn1.gif] {${\mathcal{A}}^{K}$} corresponding to weak solutions, for every micropolar parameter K ⩾ 0 denoting

    更新日期:2020-09-30
  • Transfer operator approach to ray-tracing in circular domains
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    J Slipantschuk, M Richter, D J Chappell, G Tanner, W Just and O F Bandtlow

    The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator equation for the energy density leads to an inhomogeneous equation which involves a Perron–Frobenius operator defined on a suitable Sobolev space. Even for fairly simple geometries, let alone realistic scenarios such as

    更新日期:2020-09-30
  • On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Elena Beretta, Cecilia Cavaterra and Luca Ratti

    In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining

    更新日期:2020-09-30
  • Stationary shock-like transition fronts in dispersive systems
    Nonlinearity (IF 1.505) Pub Date : 2020-09-21
    Sergey Gavrilyuk, Boniface Nkonga, Keh-Ming Shyue and Lev Truskinovsky

    We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine–Hugoniot relations to cover the case of higher order dispersive discontinuities and study their properties in an idealized case of a transition between

    更新日期:2020-09-22
  • Homogenization of biomechanical models of plant tissues with randomly distributed cells
    Nonlinearity (IF 1.505) Pub Date : 2020-09-17
    Andrey Piatnitski and Mariya Ptashnyk

    In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells and cell walls, the equations of poroelasticity for elastic deformations of plant cell walls and middle

    更新日期:2020-09-20
  • Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails
    Nonlinearity (IF 1.505) Pub Date : 2020-09-17
    Marc Kesseböhmer and Tanja I Schindler

    On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails. Under a mild mixing condition we show that the appropriately normed and trimmed sum process of these observables then converges in mean. This result is new also for the special case of i.i.d. random variables and contrasts the general case where mean convergence

    更新日期:2020-09-20
  • No solitary waves in 2D gravity and capillary waves in deep water
    Nonlinearity (IF 1.505) Pub Date : 2020-09-15
    Mihaela Ifrim and Daniel Tataru

    A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of different forces/factors influencing the fluid dynamics, e.g. gravity, surface tension or the fluid bottom. However, the existence of solitary waves has remained an open

    更新日期:2020-09-16
  • Well-posedness of the nonlinear Schrödinger equation on the half-plane
    Nonlinearity (IF 1.505) Pub Date : 2020-09-15
    A Alexandrou Himonas and Dionyssios Mantzavinos

    The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recently developed for the well-posedness of the cubic NLS equation on the half-line, which takes advantage of the solution formula produced via the unified transform of Fokas for the associated linear ibvp. For initial data in

    更新日期:2020-09-16
  • Madelung transform and probability densities in hybrid quantum–classical dynamics
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    François Gay-Balmaz and Cesare Tronci

    This paper extends the Madelung–Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid quantum–classical Lagrangian paths extending the Bohmian trajectories from standard quantum theory. As the classical symplectic form is no longer preserved, the nontrivial evolution

    更新日期:2020-09-05
  • On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    Dieter Bothe

    We consider the initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5425/nonab987dieqn1.gif] {$\dot {x}\left(t\right)=v\left(t,x\left(t\right)\right)\;\text{for}\,\;t\in \left(a,b\right),x\left({t}_{0}\right)={x}_{0}$} which determines the pathlines of a two-phase flow, i.e. v = v ( t , x ) is a given velocity field of the type ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5425/nonab987dieqn2

    更新日期:2020-09-05
  • Dimension of Gibbs measures with infinite entropy
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    Felipe Pérez Pereira

    We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an almost sure value for the symbolic dimension. We also show that the lower local dimension dimension is almost surely equal to zero, while the upper local dimension

    更新日期:2020-09-05
  • A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    Chunrong Feng, Baoyou Qu and Huaizhong Zhao

    This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system generated by a random periodic path is ergodic if and only if the underlying noise metric dynamical system at discrete time of integral multiples of the period

    更新日期:2020-09-05
  • Local well-posedness of the topological Euler alignment models of collective behavior
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    David N Reynolds and Roman Shvydkoy

    In this paper we address the problem of well-posedness of multi-dimensional topological Euler-alignment models introduced by Roman and Tadmor (2018 arXiv:1806.01371). The main result demonstrates local existence and uniqueness of classical solutions in class ( ρ , u ) ∈ H m + α × H m +1 on the periodic domain ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5176/nonab9497ieqn1.gif] {${\mathbb{T}}^{n}$}

    更新日期:2020-09-03
  • Global regularity for solutions of the three dimensional Navier–Stokes equation with almost two dimensional initial data
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    Evan Miller

    In this paper, we will prove a new result that guarantees the global existence of solutions to the Navier–Stokes equation in three dimensions when the initial data is sufficiently close to being two dimensional. This result interpolates between the global existence of smooth solutions for the two dimensional Navier–Stokes equation with arbitrarily large initial data, and the global existence of smooth

    更新日期:2020-09-03
  • Vortex lattice solutions of the ZHK Chern–Simons equations
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    K Rajaratnam and I M Sigal

    We consider the non-relativistic Chern–Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice symmetry and with topological degree one per lattice cell) similar to the Abrikosov solutions of superconductivity. We derive an asymptotic expression for the energy per

    更新日期:2020-09-03
  • Large time asymptotics for the cylindrical Korteweg–de Vries equation. I.
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    A Its and V Sukhanov

    This paper is the first part of our study the asymptotic behavior of the solutions of the cylindrical Korteweg–de Vries equation (cKdV). In this first part, we consider the solutions from Schwarz’s class and calculate the large time asymptotics using the method based on the asymptotic solution of the associated direct scattering problem. This approach was first suggested, in the cases of usual KdV

    更新日期:2020-09-03
  • Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather
    Nonlinearity (IF 1.505) Pub Date : 2020-08-26
    Yusuke Doi and Kazuyuki Yoshimura

    We construct a nonlinear lattice that has a particular symmetry in its potential function consisting of long-range pairwise interactions. The symmetry enhances smooth propagation of discrete breathers, and it is defined by an invariance of the potential function with respect to a map acting on the complex normal mode coordinates. Condition of the symmetry is given by a set of algebraic equations with

    更新日期:2020-08-27
  • Boundary-layer profile of a singularly perturbed nonlocal semi-linear problem arising in chemotaxis
    Nonlinearity (IF 1.505) Pub Date : 2020-08-26
    Chiun-Chang Lee, Zhi-An Wang and Wen Yang

    This paper is concerned with the stationary problem of an aero-taxis system with physical boundary conditions proposed by Tuval et al (2005 Proc. Natl Acad. Sci . 102 2277–82) to describe the boundary layer formation in the air–fluid interface in any dimensions. By considering a special case where fluid is free, the stationary problem is essentially reduced to a singularly perturbed nonlocal semi-linear

    更新日期:2020-08-27
  • Global solvability and stabilization to a cancer invasion model with remodelling of ECM
    Nonlinearity (IF 1.505) Pub Date : 2020-08-23
    Chunhua Jin

    In this paper, we deal with the Chaplain–Lolas’s model of cancer invasion with tissue remodelling ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5049/nonab9249ieqn1.gif] {$\left\{\begin{aligned}\hfill & {u}_{t}={\Delta}u-\chi \mathbf{\nabla }\cdot \left(u\mathbf{\nabla }v\right)-\xi \mathbf{\nabla }\cdot \left(u\mathbf{\nabla }w\right)+\mu u\left(1-u\right)+\beta uv,\hfill \\ \hfill & {v}_{t}=D{\Delta}v+u-uv

    更新日期:2020-08-24
  • Single-point blow-up in the Cauchy problem for the higher-dimensional Keller–Segel system
    Nonlinearity (IF 1.505) Pub Date : 2020-08-23
    Michael Winkler

    The Cauchy problem in ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5007/nonab9247ieqn1.gif] {${\mathbb{R}}^{n}$} for the Keller–Segel system ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5007/nonab9247ieqn2.gif] {$\begin{cases}_{t}={\Delta}u-\nabla \cdot \left(u\nabla v\right),\quad \hfill \\ {v}_{t}={\Delta}v-v+u,\quad \hfill \end{cases}$} is considered for n ⩾ 3. Using a basic theory of

    更新日期:2020-08-24
  • Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species
    Nonlinearity (IF 1.505) Pub Date : 2020-08-23
    Chueh-Hsin Chang, Chiun-Chuan Chen, Li-Chang Hung, Masayasu Mimura and Toshiyuki Ogawa

    This paper considers the problem: if coexistence occurs in the long run when a third species w invades an ecosystem consisting of two species u and v on ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5080/nonab9244ieqn1.gif] {$\mathbb{R}$} , where u , v and w compete with one another. Under the assumption that the influence of w on u and v is small and other suitable conditions, we show that the

    更新日期:2020-08-24
  • Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    Maciej J Capiński and Hieronim Kubica

    We consider perturbations of normally hyperbolic invariant manifolds, under which they can lose their hyperbolic properties. We show that if the perturbed map which drives the dynamical system preserves the properties of topological expansion and contraction, then the manifold is perturbed to an invariant set. The main feature is that our results do not require the rate conditions to hold after the

    更新日期:2020-08-06
  • On singularities of stationary isometric deformations
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    Peter Eberhard and Peter Hornung

    Unstretchable thin elastic plates such as paper can be modelled as intrinsically flat W 2,2 isometric immersions from a domain in ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn1.gif] {${\mathbb{R}}^{2}$} into ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn2.gif] {${\mathbb{R}}^{3}$} . In previous work it has been shown that if such an isometric immersion minimizes

    更新日期:2020-08-05
  • Discretization and superintegrability all rolled into one
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    A V Tsiganov

    Abelian integrals appear in mathematical descriptions of various physical processes. According to Abel’s theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are rarely used in physical applications. We propose to interpret coordinates of the fixed points either as parameters of exact discretization or as additional first integrals for equations

    更新日期:2020-08-05
  • A probabilistic Takens theorem
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    Krzysztof Barański, Yonatan Gutman and Adam Śpiewak

    Let ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4940/nonab8fb8ieqn1.gif] {$X\subset {\mathbb{R}}^{N}$} be a Borel set, μ a Borel probability measure on X and T : X → X a locally Lipschitz and injective map. Fix ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4940/nonab8fb8ieqn2.gif] {$k\in \mathbb{N}$} strictly greater than the (Hausdorff) dimension of X and assume that the set of p -periodic

    更新日期:2020-08-05
  • Bounding extrema over global attractors using polynomial optimisation
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    David Goluskin

    We present a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our approach uses (generalised) Lyapunov functions to find attracting sets, which must contain the global attractor, and the choice of Lyapunov function is optimised based

    更新日期:2020-08-05
  • Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Maria Colombo, Luigi De Rosa and Luigi Forcella

    Given any solution u of the Euler equations which is assumed to have some regularity in space—in terms of Besov norms, natural in this context—we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure p is twice as regular as u . This generalizes a recent result by Isett (2003 arXiv:1307.056517) (see also Colombo and De Rosa (2020 SIAM J. Math

    更新日期:2020-08-03
  • Rapidly rotating white dwarfs
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Walter A Strauss and Yilun Wu

    A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler–Poisson system. A white dwarf star is modeled by a very particular, and rather delicate, equation of state for the pressure as a function of the density. We prove an existence theorem for rapidly rotating

    更新日期:2020-08-03
  • Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Jana de Wiljes and Xin T Tong

    Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial–temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates

    更新日期:2020-08-03
  • A nonlinear quantum adiabatic approximation
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Clotilde Fermanian-Kammerer and Alain Joye

    This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert space of which we select a fixed basis. We study an evolution equation in which this Hamiltonian acts on the unknown vector, while depending on coordinates of the

    更新日期:2020-08-03
  • Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    C-E Pfister and W G Sullivan

    For the space X in a large class of finite alphabet shift spaces (lattice models) and the class of functions f with bounded total oscillations, we prove that each equilibrium measure ν at f = φ is a weak Gibbs measures for φ − P ( φ ). In addition, the empirical measures satisfy a full large deviations principle for ( X , ν ).

    更新日期:2020-08-03
  • Sharp time decay rates of H 1 weak solutions for the 2D MHD equations with linear damping velocity
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Hailong Ye, Yan Jia and Bo-Qing Dong

    This study is concerned with the large time decay rates of the H 1 weak solutions for the 2D magnetohydrodynamic equations with linear damping velocity. Due to the inconsistencies of the dissipative effects between linear velocity and Laplacian magnetic diffusion, neither the classic Fourier splitting method nor Kato’s method is available directly. By developing an alternative analysis argument together

    更新日期:2020-08-03
  • Well-posedness of a Schrödinger–Poisson model describing nonlinear chiral effects
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    José Luis López

    The purpose of this paper is to investigate the well-posedness in the (weighted) energy space of a Schrödinger–Poisson model with additional chiral nonlinearity proportional to the electric current ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4837/nonab8fb4ieqn1.gif] {$j\left[\psi \right]=\mathrm{I}\mathrm{m}\left(\overline{\psi }{\psi }_{x}\right)$} . More precisely, a unique mild solution of

    更新日期:2020-08-03
  • Contour dynamics for surface quasi-geostrophic fronts
    Nonlinearity (IF 1.505) Pub Date : 2020-07-28
    John K Hunter, Jingyang Shu and Qingtian Zhang

    We derive contour dynamics equations for the motion of infinite planar surface quasi-geostrophic fronts that can be represented as a graph. We give two different derivations with the same result: one is based on a decomposition of the front velocity field into a shear flow and a perturbation that decays away from the front; the other is based on the interpretation of the Riesz transform of the piecewise-constant

    更新日期:2020-07-29
  • Critical base for the unique codings of fat Sierpinski gasket
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Derong Kong and Wenxia Li

    Given β ∈ (1, 2) the fat Sierpinski gasket ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4484/nonab8bafieqn1.gif] {${\mathcal{S}}_{\beta }$} is the self-similar set in ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4484/nonab8bafieqn2.gif] {${\mathbb{R}}^{2}$} generated by the iterated function system (IFS) ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4484/nonab8bafieqn3.gif] {${f}_{\beta

    更新日期:2020-07-23
  • Third order open mapping theorems and applications to the end-point map
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Francesco Boarotto, Roberto Monti and Francesco Palmurella

    This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a finite dimensional manifold. In a second step, we compute the third order term in the Taylor expansion of the end-point map and we specialize the abstract theory to the study of length-minimality of sub-Riemannian strictly

    更新日期:2020-07-23
  • Super-critical Neumann problems on unbounded domains
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Claudianor O Alves and Abbas Moameni

    In this paper, by making use of a new variational principle, we prove existence of nontrivial solutions for two different types of semilinear problems with Neumann boundary conditions in unbounded domains. Namely, we study elliptic equations and Hamiltonian systems on the unbounded domain ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4568/nonab8bacieqn1.gif] {${\Omega}={\mathbb{R}}^{m}{\times}{B}_{r}$}

    更新日期:2020-07-23
  • Uniform recurrence properties for beta-transformation
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Lixuan Zheng and Min Wu

    For any β > 1, let T β : [0, 1) → [0, 1) be the β -transformation defined by T β x = βx mod 1. We study the uniform recurrence properties of the orbit of a point under the β -transformation to the point itself. The size of the set of points with prescribed uniform recurrence rate is obtained. More precisely, for any ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4590/nonab8a65ieqn1.gif] {$0{\leq

    更新日期:2020-07-23
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