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Some Gradient Estimates for Nonlinear Heat-Type Equations on Smooth Metric Measure Spaces with Compact Boundary 具有紧凑边界的光滑度量空间上非线性热型方程的若干梯度估计
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-08-05 DOI: 10.1007/s44198-024-00220-1
Abimbola Abolarinwa
{"title":"Some Gradient Estimates for Nonlinear Heat-Type Equations on Smooth Metric Measure Spaces with Compact Boundary","authors":"Abimbola Abolarinwa","doi":"10.1007/s44198-024-00220-1","DOIUrl":"https://doi.org/10.1007/s44198-024-00220-1","url":null,"abstract":"<p>In this paper we prove some Hamilton type and Li–Yau type gradient estimates on positive solutions to generalized nonlinear parabolic equations on smooth metric measure space with compact boundary. The geometry of the space in terms of lower bounds on the weighted Bakry–Émery Ricci curvature tensor and weighted mean curvature of the boundary are key in proving generalized local and global gradient estimates. Various applications of these gradient estimates in terms of parabolic Harnack inequalities and Liouville type results are discussed. Further consequences to some specific models informed by the nature of the nonlinearities are highlighted.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Stability of Two-Dimensional Magnetohydrodynamic System Near the Couette Flow in a Finite Channel 有限通道中库特流附近二维磁流体力学系统的渐近稳定性
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-29 DOI: 10.1007/s44198-024-00217-w
Fengjie Luo, Limei Li, Liangliang Ma
{"title":"Asymptotic Stability of Two-Dimensional Magnetohydrodynamic System Near the Couette Flow in a Finite Channel","authors":"Fengjie Luo, Limei Li, Liangliang Ma","doi":"10.1007/s44198-024-00217-w","DOIUrl":"https://doi.org/10.1007/s44198-024-00217-w","url":null,"abstract":"<p>In this paper, we consider the asymptotic stability of the incompressible two-dimensional(2D) magnetohydrodynamic(MHD) system near the Couette flow at high Reynolds number and high magnetic Reynolds number in a finite channel <span>(Omega =mathbb {T}times [-1,1])</span>. We extend the results of the Navier–Stokes equations (for the previous results see[10]) to the MHD system. We prove that if the initial velocity <span>(V_{in})</span> and the initial magnetic field <span>(B_{in})</span> satisfy <span>(Vert left( V_{in}-(y,0), B_{in}-(1,0)right) Vert _{H_{x,y}^{2}}le epsilon text {min}{nu ,mu }^frac{1}{2})</span> for some small <span>(epsilon)</span> independent of <span>(nu ,mu)</span>, then the solution of the system remains within <span>(mathcal{O}(text {min}{nu ,mu }^frac{1}{2}))</span> of Couette flow, and close to Couette flow as <span>(trightarrow infty)</span>; the magnetic field remains within <span>(mathcal{O}(text {min}{nu ,mu }^frac{1}{2}))</span> of the (1, 0), and close to (1, 0) as <span>(trightarrow infty)</span>.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-Symplectic Method for the Two-Component Camassa–Holm (2CH) System 双分量卡马萨-霍尔姆（2CH）系统的多交映法
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-18 DOI: 10.1007/s44198-024-00216-x
Xiaojian Xi, Weipeng Hu, Bo Tang, Pingwei Deng, Zhijun Qiao
{"title":"Multi-Symplectic Method for the Two-Component Camassa–Holm (2CH) System","authors":"Xiaojian Xi, Weipeng Hu, Bo Tang, Pingwei Deng, Zhijun Qiao","doi":"10.1007/s44198-024-00216-x","DOIUrl":"https://doi.org/10.1007/s44198-024-00216-x","url":null,"abstract":"<p>In this paper, the multi-symplectic formulations of the two-component Camassa–Holm system are presented. Both the multi-symplectic structure and two local conservation laws of the generalized two-component Camassa–Holm model are proposed for its first-order canonical form. Then, combining the Fourier pseudo-spectral method in the spatial domain with the midpoint method in the time dimension, the multi-symplectic Fourier pseudo-spectral scheme is constructed for the first-order canonical form. Meanwhile, the discrete scheme of the residuals of the multi-symplectic structure and two local conservation laws are also provided. By using the multi-symplectic Fourier pseudo-spectral scheme, the evolution of one- and two-soliton solutions for the generalized two-component Camassa–Holm model is regained. The structure-preserving properties and the reliability of the numerical scheme are illustrated by the tiny numerical residuals (less than 3.5 × 10<sup>−8</sup>) of the conservation laws as well as the tiny numerical variations (less than 1 × 10<sup>−9</sup>) of the amplitudes and the propagating velocities of the solitons.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141741372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Behavior and Numerical Simulations of a Conservative Phase-Field Model with Two Temperatures 双温保守相场模型的渐近行为和数值模拟
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-18 DOI: 10.1007/s44198-024-00209-w
Brice Landry Doumbe Bangola, Mohamed Ali Ipopa, Armel Andami Ovono
{"title":"Asymptotic Behavior and Numerical Simulations of a Conservative Phase-Field Model with Two Temperatures","authors":"Brice Landry Doumbe Bangola, Mohamed Ali Ipopa, Armel Andami Ovono","doi":"10.1007/s44198-024-00209-w","DOIUrl":"https://doi.org/10.1007/s44198-024-00209-w","url":null,"abstract":"<p>One of the types of problem that has attracted the attention of mathematicians in recent years is the phase field system. The field of application includes materials science, where phenomena such as phase separation in alloys, crystal formation and thermal welding are legion. Among these phase transition systems, the family of conservative systems is very popular with industry. Indeed, minimising losses in production systems is a major issue for their profitability. In this paper, we study the well-posedness of the formulation and the asymptotic behaviour of the solutions, by proving the existence of a finite-dimensional global attractor for a conservative variant of the two-temperature phase field system with homogeneous Neumann boundary conditions. The inclusion of two temperatures in the definition of the enthalpy of the system is a necessity in the case of a non-simple material. In a simple material, once the phase-change temperature has been reached, the temperature of the system remains constant until the material has completely changed state. This is not true in the case of a non-simple material, where an increase in the temperature of the system is observed even after the phase-change temperature has been reached. To conclude the work, we present a method for numerically approximating the solution and carry out some numerical tests.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Probabilistic Degenerate Fubini Polynomials Associated with Random Variables 与随机变量相关的概率退化富比尼多项式
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-10 DOI: 10.1007/s44198-024-00210-3
Rongrong Xu, Taekyun Kim, Dae San Kim, Yuankui Ma
{"title":"Probabilistic Degenerate Fubini Polynomials Associated with Random Variables","authors":"Rongrong Xu, Taekyun Kim, Dae San Kim, Yuankui Ma","doi":"10.1007/s44198-024-00210-3","DOIUrl":"https://doi.org/10.1007/s44198-024-00210-3","url":null,"abstract":"<p>Let <i>Y</i> be a random variable such that the moment generating function of <i>Y</i> exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order <i>r</i>, namely the probabilisitc degenerate Fubini polynomials associated with <i>Y</i> and the probabilistic degenerate Fubini polynomials of order <i>r</i> associated with <i>Y</i>. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of <i>Y</i>, we treat the gamma random variable with parameters <span>(alpha ,beta &gt; 0)</span>, the Poisson random variable with parameter <span>(alpha &gt; 0)</span>, and the Bernoulli random variable with probability of success <i>p</i>.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A General Coupled Derivative Nonlinear Schrödinger System: Darboux Transformation and Soliton Solutions 一般耦合衍生非线性薛定谔系统：达尔布变换和孤子解
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-09 DOI: 10.1007/s44198-024-00212-1
Yonghui Kuang
{"title":"A General Coupled Derivative Nonlinear Schrödinger System: Darboux Transformation and Soliton Solutions","authors":"Yonghui Kuang","doi":"10.1007/s44198-024-00212-1","DOIUrl":"https://doi.org/10.1007/s44198-024-00212-1","url":null,"abstract":"<p>In this work we present a general coupled derivative nonlinear Schrödinger system. We construct the corresponding <i>N</i>-fold Darboux transform and generalized Darboux transform. Under this construction, we give different soliton solutions and plot their figures describing the soliton characteristics and dynamical behaviors, including higher-order soliton and rouge wave solution etc.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Common Borel Direction of Entire Function f and Its q-Difference Operator 论全函数 f 及其 q-差分算子的共 Borel 方向
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-02 DOI: 10.1007/s44198-024-00205-0
Zhigao Qin, Jianren Long, Ling Wang
{"title":"On Common Borel Direction of Entire Function f and Its q-Difference Operator","authors":"Zhigao Qin, Jianren Long, Ling Wang","doi":"10.1007/s44198-024-00205-0","DOIUrl":"https://doi.org/10.1007/s44198-024-00205-0","url":null,"abstract":"<p>The common Borel direction of entire function <i>f</i>(<i>z</i>) and its <i>q</i>-difference operator is studied by using Nevanlinna theory. Some conditions of the existence of common Borel direction for entire function <i>f</i>(<i>z</i>) and its <i>q</i>-difference operator are obtained in this paper.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Temporal Tweezing of Cavity Solitons 关于腔隙孤子的时空镊合
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-02 DOI: 10.1007/s44198-024-00193-1
Julia Rossi, Sathyanarayanan Chandramouli, Ricardo Carretero-González, Panayotis G. Kevrekidis
{"title":"On the Temporal Tweezing of Cavity Solitons","authors":"Julia Rossi, Sathyanarayanan Chandramouli, Ricardo Carretero-González, Panayotis G. Kevrekidis","doi":"10.1007/s44198-024-00193-1","DOIUrl":"https://doi.org/10.1007/s44198-024-00193-1","url":null,"abstract":"<p>Motivated by the work of Jang et al., Nat Commun 6:7370 (2015), where the authors experimentally tweeze cavity solitons in a passive loop of optical fiber, we study the amenability to tweezing of cavity solitons as the properties of a localized tweezer are varied. The system is modeled by the Lugiato-Lefever equation, a variant of the complex Ginzburg-Landau equation. We produce an effective, localized, trapping tweezer potential by assuming a Gaussian phase-modulation of the holding beam. The potential for tweezing is then assessed as the total (temporal) displacement and speed of the tweezer are varied, and corresponding phase diagrams are presented. As the relative speed of the tweezer is increased we find two possible dynamical scenarios: successful tweezing and release of the cavity soliton. We also deploy a non-conservative variational approximation (NCVA) based on a Lagrangian description which reduces the original dissipative partial differential equation to a set of coupled ordinary differential equations for the cavity soliton parameters. We illustrate the ability of the NCVA to accurately predict the separatrix between successful and failed tweezing. This showcases the versatility of the NCVA to provide a low-dimensional description of the experimental realization of the temporal tweezing.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of Regular Solutions for a Class of Incompressible Non-Newtonian MHD Equations Coupled to the Heat Equation 一类与热方程耦合的不可压缩非牛顿多流体力学方程常规解的存在性
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-07-02 DOI: 10.1007/s44198-024-00211-2
Rina Su, Changjia Wang
{"title":"Existence of Regular Solutions for a Class of Incompressible Non-Newtonian MHD Equations Coupled to the Heat Equation","authors":"Rina Su, Changjia Wang","doi":"10.1007/s44198-024-00211-2","DOIUrl":"https://doi.org/10.1007/s44198-024-00211-2","url":null,"abstract":"<p>We consider a system of PDE’s describing the steady flow of an electrically conducting fluid in the presence of a magnetic field. The system of governing equations composes of the stationary non-Newtonian incompressible MHD equations coupled to the heat equation wherein the influence of buoyancy is taken into account in the momentum equation and the Joule heating and viscous heating terms are included. We proved the existence of <span>(C^{1,gamma }({bar{Omega }})times W^{2,r}(Omega )times W^{2,2}{(Omega )})</span> solutions of the systems for <span>(1&lt; p&lt;2)</span> corresponding to a small data and we show that this solution is unique in case <span>(6/5&lt; p &lt; 2)</span>. Moreover, we also proved the higher regularity properties of this solution.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral Solutions of Specific Singular Differential Equations Using A Unified Spectral Galerkin-Collocation Algorithm 使用统一谱 Galerkin-Collocation 算法的特定奇异微分方程谱解法
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-27 DOI: 10.1007/s44198-024-00194-0
H. M. Ahmed, W. M. Abd-Elhameed
{"title":"Spectral Solutions of Specific Singular Differential Equations Using A Unified Spectral Galerkin-Collocation Algorithm","authors":"H. M. Ahmed, W. M. Abd-Elhameed","doi":"10.1007/s44198-024-00194-0","DOIUrl":"https://doi.org/10.1007/s44198-024-00194-0","url":null,"abstract":"<p>This paper presents a novel numerical approach to addressing three types of high-order singular boundary value problems. We introduce and consider three modified Chebyshev polynomials (CPs) of the third kind as proposed basis functions for these problems. We develop new derivative operational matrices for the three modified CPs of the third kind by deriving formulas for their first derivatives. Our approach follows a unified method for numerically handling singular differential equations (DEs). To transform these equations into algebraic systems suitable for numerical treatment, we employ the collocation method in combination with the introduced operational matrices of derivatives of the modified CPs of the third kind. We address the convergence examination for the three expansions in a unified manner. We present numerous numerical examples to demonstrate the accuracy and efficiency of our unified numerical approach.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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