Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Solvability of functional third-order problems of Ambrosetti–Prodi-type","authors":"","doi":"10.1016/j.cnsns.2024.108312","DOIUrl":"10.1016/j.cnsns.2024.108312","url":null,"abstract":"<div><p>This work presents an Ambrosetti–Prodi alternative for functional problems composed of a fully third-order differential equation with two types of functional boundary conditions. The discussion of existence and non-existence of solution is obtained in a more general case, and the multiplicity of solution is done with restrictive boundary conditions-</p><p>The main arguments are based on the lower and upper solutions method, together with the Leray–Schauder topological degree theory. We stress that the multiplicity situation requires different speed growths on the variables.</p><p>An example illustrates the results’ applicability and shows a technique to estimate the bifurcation values of the parameter.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424004970/pdfft?md5=2bc343354edcd4d4858deee8d127d2dd&pid=1-s2.0-S1007570424004970-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Magneto-photo-thermoelastic influences on a semiconductor hollow cylinder via a series-one-relaxation model","authors":"","doi":"10.1016/j.cnsns.2024.108295","DOIUrl":"10.1016/j.cnsns.2024.108295","url":null,"abstract":"<div><p>This article discusses the deformation of semiconductor cylinders in the context of photothermoelastic theory. The proposed model is used to describe thermal waves, plasma waves, and elastic waves and analyze the theoretical analysis of thermal deformation effects on semiconductor hollow cylinders. The interior of the hollow cylinder is clamped and unaffected by thermal loads and carrier concentrations, while the exterior is subject to sinusoidal heating and limited carrier density. In addition, the surface of the cylinder is surrounded by magnets in the direction of its axis. Initially, the governing equations are explained in Laplace domain and the Laplace inversion is used numerically. The results from thermal physics are presented graphically to investigate the impact of thermal relaxation and temperature on temperature of plasma thermoelastic waves. The effects of carrier diffusion coefficient and surface recombination rate on carrier concentration distribution are also discussed in detail.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083693","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}

{"title":"Measurement of safety state of cross-jointed segmental lining based on system performance index","authors":"","doi":"10.1016/j.cnsns.2024.108304","DOIUrl":"10.1016/j.cnsns.2024.108304","url":null,"abstract":"<div><p>The correlation between convergence deformation and the safety state of a cross-jointed segmental lining is investigated and clarified. The limitations of convergence deformation as a measuring scale is explored also. Firstly, an analytical algorithm (known as the relative stiffness method, RSM) is developed and verified for tracing the mechanical response of a cross-jointed segmental lining in failure history. Then, an explicit mapping relationship between convergence deformation and the causal factors is established using the RSM. Finally, the root causes of the limitations in using convergence deformation as a scale to evaluate tunnel safety state are discussed, and an alternative quantity, the system performance index (SPI), is proposed. It shows that: (1) The convergence deformation consists of three components induced by segment bending, elastic joint rotation, and joint stiffness attenuating, respectively. The deformation induced by attenuating joint stiffness is dependent on the failure index of segment joints and provides crucial information about the load-bearing state of the segment joints; (2) The components of elastic joint rotation and joint stiffness attenuating are significantly affected by the contact stiffness of the segment joint interface, including the physical and mechanical properties of the packing material. The magnitudes of convergence deformation and its components are not suitable for use as a quantitative scale to evaluate the safety state of the lining due to their inherent drawbacks; (3) The proposed dimensionless variable SPI can eliminate the influence of packing material on the safety state of the segment lining and reflect the comprehensive influence of the failure indexes of the segment joints.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097875","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}

{"title":"Non-ergodic convergence rate of an inertial accelerated primal–dual algorithm for saddle point problems","authors":"","doi":"10.1016/j.cnsns.2024.108289","DOIUrl":"10.1016/j.cnsns.2024.108289","url":null,"abstract":"<div><p>In this paper, we design an inertial accelerated primal–dual algorithm to address the convex–concave saddle point problem, which is formulated as <span><math><mrow><msub><mrow><mo>min</mo></mrow><mrow><mi>x</mi></mrow></msub><msub><mrow><mo>max</mo></mrow><mrow><mi>y</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mrow><mo>〈</mo><mi>K</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></mrow><mo>−</mo><mi>g</mi><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span>. Remarkably, both functions <span><math><mi>f</mi></math></span> and <span><math><mi>g</mi></math></span> exhibit a composite structure, combining “nonsmooth” ＋ “smooth” components. Under the assumption of partially strong convexity in the sense that <span><math><mi>f</mi></math></span> is convex and <span><math><mi>g</mi></math></span> is strongly convex, we introduce a novel inertial accelerated primal–dual algorithm based on Nesterov’s extrapolation. This algorithm can be reduced to two classical accelerated forward–backward methods for unconstrained optimization problem. We show that the proposed algorithm achieves a non-ergodic <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> convergence rate, where <span><math><mi>k</mi></math></span> represents the number of iterations. Several numerical experiments validate the efficiency of our proposed algorithm.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S100757042400474X/pdfft?md5=1e9e5c48fc9e2a5ef1beb31a18232e80&pid=1-s2.0-S100757042400474X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Self-spinning of liquid crystal elastomer tubes under constant light intensity","authors":"","doi":"10.1016/j.cnsns.2024.108296","DOIUrl":"10.1016/j.cnsns.2024.108296","url":null,"abstract":"<div><p>Self-oscillating motion have the capacity to autonomously converting ambient power into repetitive motion without requiring an additional control unit, and designing more self-oscillating can broaden their utilization in energy extraction, robotic systems, and sensors. However, cyclic self-oscillating motions often cause structural instability and increase friction. To address these challenges, we creatively developed a zero-energy-mode self-spinning liquid crystal elastomer (LCE) tube-mass system under constant light intensity. By proposing a nonlinear dynamic model and using fourth-order Runge-Kutta method, the computational findings suggest that the LCE tube stays stationary when exposed to vertical light while develops into a zero-energy-mode self-spinning state under non-vertical light. The self-spinning state is self-sustained through harvesting ambient light energy, helping counteract the damping loss. In addition, the self-spinning frequency is controllable by tuning the light angle, contraction coefficient, light intensity, elastic modulus, radius, and damping coefficient. The translational damping has no impact on the self-spinning frequency, and the elastic modulus does not affect the X-axis displacement of the free end. The proposed self-spinning LCE tube system, differing from numerous existing self-oscillating systems, offers advantages like zero-energy-mode motion, structural simplicity, and controllability across multiple parameters, promising expanded design opportunities for applications such as motors, soft robotics, energy collectors, micro-machines, and beyond.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088307","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}

{"title":"On a Schrödinger equation involving fractional (N/s1,q)-Laplacian with critical growth and Trudinger–Moser nonlinearity","authors":"","doi":"10.1016/j.cnsns.2024.108284","DOIUrl":"10.1016/j.cnsns.2024.108284","url":null,"abstract":"<div><p>A nonlinear Schrödinger equation of fractional <span><math><mrow><mo>(</mo><mi>N</mi><mo>/</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplacian is considered with the Rabinowitz potential, critical Sobolev growth and Trudinger–Moser nonlinearity in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> <span><span><span><math><mrow><msubsup><mrow><mfenced><mrow><mo>−</mo><mi>Δ</mi></mrow></mfenced></mrow><mrow><mi>N</mi><mo>/</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mi>u</mi><mo>+</mo><msubsup><mrow><mfenced><mrow><mo>−</mo><mi>Δ</mi></mrow></mfenced></mrow><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>ɛ</mi><mi>x</mi><mo>)</mo></mrow><mrow><mo>(</mo><mrow><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>N</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>λ</mi><mi>f</mi><mfenced><mrow><mi>u</mi></mrow></mfenced><mo>+</mo><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><msubsup><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>.</mo></mrow></math></span></span></span>We establish the global existence of nonnegative ground-state solution for suitable parameter values primarily through variational analysis, fractional Trudinger–Moser inequality and mountain pass approach. It is a crucial ingredient to handle three aspects concerning the limiting setting <span><math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi><mo>=</mo><mi>N</mi></mrow></math></span>, the critical Sobolev growth and Trudinger–Moser nonlinearity.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006648","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}

{"title":"L1-FEM discretizations for two-dimensional multiterm fractional delay diffusion equations","authors":"","doi":"10.1016/j.cnsns.2024.108285","DOIUrl":"10.1016/j.cnsns.2024.108285","url":null,"abstract":"<div><p>A two-dimensional multiterm fractional delay diffusion equation is considered. The representation of the exact solution of the equation is derived and it is shown that the solution exhibits singular behaviors at multiple nodes due to the initial singularity and time delay. This results in the numerical schemes for solving the equation typically have a lower order of convergence in time. The problem is approximated in time by the L1 and Alikhanov schemes on symmetrical graded meshes, while in space the standard finite element method is applied. Numerical stability and convergence are presented for the schemes. Numerical experiments are performed to show the effectiveness of the schemes.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142039800","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}

{"title":"Novel multi-step predictor–corrector schemes for backward stochastic differential equations","authors":"","doi":"10.1016/j.cnsns.2024.108269","DOIUrl":"10.1016/j.cnsns.2024.108269","url":null,"abstract":"<div><p>Novel multi-step predictor–corrector numerical schemes have been derived for approximating decoupled forward–backward stochastic differential equations. The stability and high order rate of convergence of the proposed schemes are rigorously proved. We also present a sufficient and necessary condition for the stability of the schemes. Numerical experiments are given to illustrate the stability and convergence rates of the proposed methods.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020696","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}

{"title":"Mathematical study of a new coupled electro-thermo radiofrequency model of cardiac tissue","authors":"","doi":"10.1016/j.cnsns.2024.108281","DOIUrl":"10.1016/j.cnsns.2024.108281","url":null,"abstract":"<div><p>This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141998804","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}

{"title":"A novel multi-frame image super-resolution model based on regularized nonlinear diffusion with Caputo time fractional derivative","authors":"","doi":"10.1016/j.cnsns.2024.108280","DOIUrl":"10.1016/j.cnsns.2024.108280","url":null,"abstract":"<div><p>In this work, we introduce an innovative fractional nonlinear parabolic model using a time-fractional order derivative, specifically employing the <em>Caputo</em> sense for fractional differentiation. This model aims to enhance traditional super-resolution models, particularly in the context of multi-frame image super-resolution. Additionally, we incorporate a regularized Perona–Malik diffusion mechanism to control the speed and direction of diffusion at each image location. We begin our study by exploring the theoretical solvability of our proposed model. Firstly, we employ the <em>Faedo–Galerkin</em> approach to establish the existence and uniqueness of a weak solution for an auxiliary fractional super-resolution model. Subsequently, we use the Schauder fixed point method to demonstrate the existence and uniqueness of a weak solution for our model. To validate the effectiveness of our model in the multi-frame super-resolution (SR) context, we conduct numerical experiments on images featuring diverse characteristics, including corners and edges, while applying various warping, decimation, and blurring matrices to the low-resolution (LR) images. We start the evaluation by introducing an adaptive discrete scheme tailored to the proposed model. To prove the robustness of our approach, we subject our images to varying levels of noise. Additionally, we perform simulations on real data (videos). The obtained high-resolution (HR) results demonstrate notable efficiency and robustness against noise, outperforming competitive models both visually and quantitatively.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012979","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}