Partial Differential Equations in Applied Mathematics最新文献_第8页

An immersed interface method for nonlinear convection–diffusion equations with interfaces 具有界面的非线性对流扩散方程的浸入界面法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-11 DOI: 10.1016/j.padiff.2025.101250

Miguel Uh Zapata , Reymundo Itza Balam , Silvia Jerez

引用次数: 0

Local dynamics of second-order differential equation with delayed derivative 二阶时滞微分方程的局部动力学

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-09-02 DOI: 10.1016/j.padiff.2025.101281

Ilia Kashchenko, Igor Maslenikov

{"title":"Local dynamics of second-order differential equation with delayed derivative","authors":"Ilia Kashchenko, Igor Maslenikov","doi":"10.1016/j.padiff.2025.101281","DOIUrl":"10.1016/j.padiff.2025.101281","url":null,"abstract":"<div><div>We study the nonlinear dynamics of second-order differential equation with delayed feedback depending on the derivative. The problem in question contains a small multiplier at the highest derivative, so it is singularly perturbed. We determine the stability of equilibrium depending on the parameters and find critical (bifurcation) cases. In each critical case, asymptotic approximations for the spectrum points (roots of the characteristic equation) are determined. The main feature of the problem under consideration is that in critical cases the spectrum consists of two parts: an infinite chain of points that tend to the imaginary axis and one or two more points located near the imaginary axis.</div><div>Using methods of asymptotic analysis to study bifurcations, in the critical cases we construct special equations – quasinormal forms. Quasinormal form is an analog of normal form. It does not depends on small parameter and its solutions provide the main part of the asymptotic approximation of the solutions of the original problem. Each quasinormal form is a partial differential equation with an antiderivative operator and integral term in nonlinearity. For the constructed forms stable periodic solutions are determined, asymptotic approximations on stable periodic solutions of original problem is obtained and the bifurcations that occur are described.</div><div>Also, the situation where two successive bifurcations occur in the system was described.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101281"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 of dark multi-solitons to the intermediate nonlinear Schrödinger equation 暗多孤子对中间非线性Schrödinger方程的渐近行为

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-29 DOI: 10.1016/j.padiff.2025.101273

Takafumi Akahori

引用次数: 0

The impact of carbon nanotubes (CNT) on heat generation and absorption, the behaviour of water and blood suspensions in an inclined channel with a porous matrix 碳纳米管（CNT）对热产生和吸收的影响，水和血液悬浮液在多孔基质倾斜通道中的行为

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-26 DOI: 10.1016/j.padiff.2025.101241

Mangala Kandagal , Ramesh Kempepatil , Jagadish V. Tawade , Nodira Nazarova , Manish Gupta , M. Khan

{"title":"The impact of carbon nanotubes (CNT) on heat generation and absorption, the behaviour of water and blood suspensions in an inclined channel with a porous matrix","authors":"Mangala Kandagal , Ramesh Kempepatil , Jagadish V. Tawade , Nodira Nazarova , Manish Gupta , M. Khan","doi":"10.1016/j.padiff.2025.101241","DOIUrl":"10.1016/j.padiff.2025.101241","url":null,"abstract":"<div><div>The study investigates the heat generation and absorption of engine oil, human blood and single wall carbon Nano tube (SWCNT) in an inclined channel filled with a porous matrix. Two regions are considered, both regions are of porous medium. Due to their enhanced thermal conductivity, are utilized to improve heat transfer efficiency in various applications. Formulation of the problem is framed using conservation of mass, energy and momentum in both regions. The flow of oil, human blood through a porous medium is analysed, considering the effects of both heat generation and absorption within the system. Key parameters such as the inclination angle of the channel, the porosity and the type of fluids are examined to understand their impact on the overall heat transfer process and velocity. To solve the problem regular perturbation method is applied for non-dimensional quantities; The presence of CNTs significantly improves the thermal conductivity of both engine oil and blood suspensions, leading to improved heat dissipation or absorption capabilities, which are influenced by the inclination and the porous structure. This study offers valuable insights into fluid flow processes in the human body using Nanotubes. Influence of CNTs on the fluid flow of human body and heat generation/absorption with porous matrix in both regions is unsolved problem.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101241"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 exact explicit solutions and conservation laws of the generalized (3+1)-D Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity 幂律非线性广义(3+1)-D Camassa-Holm-Kadomtsev-Petviashvili方程的精确显式解和守恒律

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-28 DOI: 10.1016/j.padiff.2025.101257

Thokozani Blessing Shiba, Khadijo Rashid Adem

引用次数: 0

Numerical approximation of time-fractional nonlinear partial integro-differential equation using fractional Euler and cubic trigonometric B-Spline methods 用分数阶欧拉和三次三角b样条方法数值逼近时间分数阶非线性偏积分微分方程

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-02 DOI: 10.1016/j.padiff.2025.101223

Mehwish Saleem , Arshed Ali , Fazal-i-Haq , Hassan Khan

{"title":"Numerical approximation of time-fractional nonlinear partial integro-differential equation using fractional Euler and cubic trigonometric B-Spline methods","authors":"Mehwish Saleem , Arshed Ali , Fazal-i-Haq , Hassan Khan","doi":"10.1016/j.padiff.2025.101223","DOIUrl":"10.1016/j.padiff.2025.101223","url":null,"abstract":"<div><div>Nonlinear mathematical problems arise due to existence of important complex nonlinear phenomena in engineering and science. In this article, a class of time-fractional nonlinear parabolic partial integro-differential equations is solved numerically by combination of fractional Euler and cubic trigonometric B-spline collocation methods. Backward finite difference formula is employed for time-fractional Caputo derivative to get an unconditional stable scheme. The memory(integral) term is evaluated using a second order quadrature rule. Fractional Euler method for Caputo derivative is used in computing the nonlinear memory term. At each time level, cubic trigonometric B-spline functions are applied to obtain the solution in spatial dimension which reduces the problem to a system of algebraic equations. This method has the ability to handle any kind of nonlinearity without using iterative processes. Efficiency and reliability of the current method is analyzed for the fractional-order via three highly nonlinear test problems with variable coefficients. The rate of convergence of the proposed method is also computed in temporal and spatial dimensions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101223"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploring spectral collocation methods for diffusion models with variable coefficients in heat transfer studies 探讨换热研究中变系数扩散模型的谱配置方法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-01-28 DOI: 10.1016/j.padiff.2025.101097

Ihteram Ali , Nadia Kamal , Abdulrahman Obaid Alshammari , Rahman Ullah , Imtiaz Ahmad

{"title":"Exploring spectral collocation methods for diffusion models with variable coefficients in heat transfer studies","authors":"Ihteram Ali , Nadia Kamal , Abdulrahman Obaid Alshammari , Rahman Ullah , Imtiaz Ahmad","doi":"10.1016/j.padiff.2025.101097","DOIUrl":"10.1016/j.padiff.2025.101097","url":null,"abstract":"<div><div>The diffusion equation with variable coefficients is widely applied in heat transfer to model the distribution of temperature in materials with spatially varying thermal properties, allowing for accurate simulation of heat conduction in heterogeneous media, accounting for changes in material composition and thermal conductivity. In this work, an effective method for numerically solving the one-dimensional diffusion equation with variable coefficients is presented. This approach utilizes a hybrid method that combines Lucas and Fibonacci polynomials with finite differences to convert the problem into a time-discrete form using the forward finite difference approach. Then, the derivative of the function is estimated using Fibonacci polynomials. The proposed method is applied to both linear and nonlinear one-dimensional problems, and its efficacy is verified by comparing the obtained results with those of alternative methods. The accuracy and effectiveness of the proposed method are demonstrated through comparison with the exact solution and other methods found in the literature.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101097"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A generalized (2+1)-dimensional generalized KdV equation with a plethora of analytical solutions and conservation laws 具有大量解析解和守恒律的广义（2+1）维广义KdV方程

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-06 DOI: 10.1016/j.padiff.2025.101233

M.C. Sebogodi , A.R. Adem , B. Muatjetjeja

引用次数: 0

Some novel properties of complex intuitionistic fuzzy ideals in classical ring 经典环中复杂直觉模糊理想的一些新性质

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-07 DOI: 10.1016/j.padiff.2024.100811

Ziad Khan , Fawad Hussain , Ikhtesham Ullah , Tariq Rahim , Madad Khan , Rashid Jan , Ibrahim Mekawy , Asma Alharbi

{"title":"Some novel properties of complex intuitionistic fuzzy ideals in classical ring","authors":"Ziad Khan , Fawad Hussain , Ikhtesham Ullah , Tariq Rahim , Madad Khan , Rashid Jan , Ibrahim Mekawy , Asma Alharbi","doi":"10.1016/j.padiff.2024.100811","DOIUrl":"10.1016/j.padiff.2024.100811","url":null,"abstract":"<div><div>The complex intuitionistic fuzzy set is an extension of the intuitionistic fuzzy set where the membership and non-membership functions are expressed by a complex numbers. Ring theory is a well-known field of abstract algebra that is used in a broad area of present study in mathematics and computer science. The study of ideals is important in numerous ways in ring theory. Keeping in view the importance of complex intuitionistic fuzzy sets and ring theory, in this paper, we define the notion of complex intuitionistic fuzzy ideals in a classical ring <span><math><mi>R</mi></math></span> and investigate its various algebraic properties. We obtain that the intersection of any two complex intuitionistic fuzzy ideals of a classical ring <span><math><mi>R</mi></math></span> is again a complex intuitionistic fuzzy ideal of <span><math><mi>R</mi></math></span>. We also define the notion of a complex intuitionistic fuzzy level set. Furthermore, we define the concept of complex intuitionistic fuzzy cosets of a complex intuitionistic fuzzy ideal of a classical ring and prove that the set of all complex intuitionistic fuzzy cosets of a complex intuitionistic fuzzy ideal forms a ring under certain binary operations. Finally, we prove a complex intuitionistic fuzzy version of the fundamental theorem of a ring homomorphism.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 100811"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144842010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analytical new soliton solutions and stability analysis of the (2 + 1)-dimensional time-fractional nonlinear GZKBBM equation （2 + 1）维时间分数阶非线性GZKBBM方程的解析新孤子解及稳定性分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-03 DOI: 10.1016/j.padiff.2025.101256

Nazia Parvin , Hasibun Naher , M. Ali Akbar

{"title":"Analytical new soliton solutions and stability analysis of the (2 + 1)-dimensional time-fractional nonlinear GZKBBM equation","authors":"Nazia Parvin , Hasibun Naher , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101256","DOIUrl":"10.1016/j.padiff.2025.101256","url":null,"abstract":"<div><div>In this study, we investigate the soliton solutions of the (2 + 1)-dimensional time-fractional nonlinear generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation using the extended sinh-Gordon expansion approach. This equation is useful in modeling the hydro-magnetic waves in cold plasma, acoustic waves in harmonic crystals, shallow water waves, and acoustic gravity waves. By utilizing the suggested approach, we derive some rich structured soliton solutions, including bell-shaped soliton, anti-bell-shaped soliton, anti-peakon, periodic soliton and singular solitons of the model. These solutions are expressed in hyperbolic and trigonometric forms, and their dynamical behaviors are illustrated through 3D and 2D plots for various values of the fractional parameter <span><math><mrow><mi>β</mi><mspace></mspace></mrow></math></span>and other physical parameters. The impact of the time-fractional derivative on the introduced model is examined using the beta derivative framework, which provides a more general and flexible way to enhance the accuracy of the solutions. The stability of the model is also examined through the linear stability theory, confirming that all analytical findings are stable. The results unambiguously demonstrate that the extended sinh-Gordon expansion approach is compatible, reliable, and efficient for investigating various nonlinear evolution equations in fields of applied science and engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101256"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0