Journal of Differential Equations最新文献_第3页

Gauge transformation for the kinetic derivative nonlinear Schrödinger equation on the torus 环面上动力学导数非线性Schrödinger方程的规范变换

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-23 DOI: 10.1016/j.jde.2025.113792

Nobu Kishimoto , Yoshio Tsutsumi

引用次数: 0

On a fractional semilinear Neumann problem arising in Chemotaxis 趋化性中的一个分数阶半线性Neumann问题

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-22 DOI: 10.1016/j.jde.2025.113779

Eleonora Cinti, Matteo Talluri

引用次数: 0

Conditional sofic mean dimension 条件平均维数

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-22 DOI: 10.1016/j.jde.2025.113785

Bingbing Liang

引用次数: 0

On computations of Poincaré-Dulac normal forms 关于poincar_3 - dulac范式的计算

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-22 DOI: 10.1016/j.jde.2025.113781

Tatjana Petek , Valery G. Romanovski

{"title":"On computations of Poincaré-Dulac normal forms","authors":"Tatjana Petek , Valery G. Romanovski","doi":"10.1016/j.jde.2025.113781","DOIUrl":"10.1016/j.jde.2025.113781","url":null,"abstract":"<div><div>There are two approaches to computing Poincaré-Dulac normal forms of systems of ODEs. Under the original approach used by Poincaré and Dulac the normalizing transformation is explicitly computed. On each step, the normalizing procedure requires the substitution of a polynomial into a series. Under the other approach, a normal form is computed using Lie transformations. In this case, the changes of coordinates are performed as actions of certain infinitesimal generators. In both cases, on each step the homological equation is solved in the vector space of polynomial vector fields <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> where each component of the vector field is a homogeneous polynomial of degree <em>j</em>. We present a novel approach which leads to two new algorithms for normal form computations. The first one is designed for polynomial systems of ODEs in which the coefficients of all terms are treated as parameters. While our method employs Lie transformations, the homological equation is solved not in <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> but in the vector space of polynomial vector fields where each component is a homogeneous polynomial in the parameters of the system. It is shown that the space of the parameters is a kind of dual space and the computation of normal forms can be performed in the space of parameters treated as the space of generalized vector fields, which we call the lattice vector fields. The second algorithm applies to any analytic or formal autonomous system of ODEs and offers one of the simplest normal form computation methods available in the literature. Remarkably, the procedure involves only arithmetic operations with scalars, significantly simplifying the computational process.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113781"},"PeriodicalIF":2.3,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Smooth Koopman eigenfunctions 光滑库普曼特征函数

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-22 DOI: 10.1016/j.jde.2025.113786

Suddhasattwa Das

{"title":"Smooth Koopman eigenfunctions","authors":"Suddhasattwa Das","doi":"10.1016/j.jde.2025.113786","DOIUrl":"10.1016/j.jde.2025.113786","url":null,"abstract":"<div><div>Any dynamical system, whether it is generated by a differential equation or a transformation map on a manifold, induces a dynamics on functional-spaces. The choice of functional-space may vary, but the induced dynamics is always linear, and codified by the Koopman operator. The eigenfunctions of the Koopman operator are of extreme importance in the study of the dynamics. They provide a clear distinction between the mixing and non-mixing components of the dynamics, and also reveal embedded toral rotations. The usual choice of functional-space is <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, a class of square integrable functions. A fundamental problem with eigenfunctions in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is that they are often extremely discontinuous, particularly if the system is chaotic. There are some prototypical systems called skew-product dynamics in which <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> Koopman eigenfunctions are also smooth. The article shows that under general assumptions on an ergodic system, these prototypical examples are the only possibility. Moreover, the smooth eigenfunctions can be used to create a change of variables which explicitly characterizes the weakly mixing component too.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113786"},"PeriodicalIF":2.3,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Weak and mild solutions to the MHD equations and the viscoelastic Navier–Stokes equations with damping in Wiener amalgam spaces Wiener汞合金空间中MHD方程和带阻尼的粘弹性Navier-Stokes方程的弱解和温和解

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-18 DOI: 10.1016/j.jde.2025.113777

Chen-Chih Lai

引用次数: 0

Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay 时变或状态相关时滞微分方程循环系统的离散Lyapunov泛函

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-17 DOI: 10.1016/j.jde.2025.113768

István Balázs , Ábel Garab

引用次数: 0

Thermo-elasticity problems with evolving microstructures 微观结构演化的热弹性问题

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-16 DOI: 10.1016/j.jde.2025.113764

Michael Eden , Adrian Muntean

{"title":"Thermo-elasticity problems with evolving microstructures","authors":"Michael Eden , Adrian Muntean","doi":"10.1016/j.jde.2025.113764","DOIUrl":"10.1016/j.jde.2025.113764","url":null,"abstract":"<div><div>We consider the mathematical analysis and homogenization of a moving boundary problem posed for a highly heterogeneous, periodically perforated domain. More specifically, we are looking at a one-phase thermo-elasticity system with phase transformations where small inclusions, initially periodically distributed, are growing or shrinking based on a kinetic under-cooling-type law and where surface stresses are created based on the curvature of the phase interface. This growth is assumed to be uniform in each individual cell of the perforated domain. After transforming to the initial reference configuration (utilizing the Hanzawa transformation), we use the contraction mapping principle to show the existence of a unique solution for a possibly small but <em>ε</em> independent time interval (<em>ε</em> is here the scale of heterogeneity).</div><div>In the homogenization limit, we recover a macroscopic thermo-elasticity problem which is strongly non-linearly coupled (via an internal parameter called height function) to local changes in geometry. As a direct by-product of the mathematical analysis work, we present an alternative equivalent formulation which lends itself to an effective pre-computing strategy that is very much needed as the limit problem is computationally expensive.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113764"},"PeriodicalIF":2.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fine boundary regularity for fully nonlinear mixed local-nonlocal problems 完全非线性混合局部-非局部问题的精细边界正则性

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-16 DOI: 10.1016/j.jde.2025.113780

Mitesh Modasiya, Abhrojyoti Sen

引用次数: 0

Travelling wave solutions to a microtube-driven glioma invasion model 微管驱动胶质瘤侵袭模型的行波解决方案

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-16 DOI: 10.1016/j.jde.2025.113759

Ryan Thiessen, Thomas Hillen

{"title":"Travelling wave solutions to a microtube-driven glioma invasion model","authors":"Ryan Thiessen, Thomas Hillen","doi":"10.1016/j.jde.2025.113759","DOIUrl":"10.1016/j.jde.2025.113759","url":null,"abstract":"<div><div>In this article, we establish the existence of travelling wave solutions for a non-cooperative reaction-diffusion model representing glioma cell invasion. The model describes the microtube-driven migration of glioma consisting of an ODE equation describing the dynamics of the tumour bulk and a reaction-diffusion equation for the tumour microtubes. We derive an explicit formula for the minimum wave speed <span><math><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> based on system parameters such that travelling waves exist for speeds <span><math><mi>c</mi><mo>≥</mo><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> while no travelling wave solution exists for <span><math><mi>c</mi><mo><</mo><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>. We prove the existence of travelling wave solutions by constructing upper and lower solutions and employing Schauder's fixed point theorem. We obtain non-existence for small speeds by use of the negative one-sided Laplace transform. Our result is one of the few complete results on travelling waves of a non-cooperative partially degenerate reaction-diffusion systems. The findings have implications for understanding glioma spread dynamics and potential modelling applications in predicting tumour progression based on cellular migration speeds.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113759"},"PeriodicalIF":2.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0