Pub Date : 2024-12-19DOI: 10.1016/j.cnsns.2024.108550
I. Cavallari, J. Feng, M. Vasile
The paper introduces an averaged model suitable for studying the long-term attitude dynamics of low Earth orbit objects subject to the interaction with the exosphere. This work extends previous results by the authors on the development of a semi-analytical theory for long-term attitude propagation. The first-order averaged model is developed by expressing the rotational problem in modified Sadov variables and performing the average of the equations of motion over the fast Sadov angles and the orbital mean anomaly. A transformation from osculating to mean variables is also derived from a combination of Lie transformations. The approach proposed in this paper is applied to two possible atmospheric drag models: a simple, commonly used, model characterised by a constant dimensionless drag coefficient and a higher fidelity model based on the theory by Sentman (1961).
{"title":"Semi-analytical attitude propagation of low-altitude Earth orbiting objects","authors":"I. Cavallari, J. Feng, M. Vasile","doi":"10.1016/j.cnsns.2024.108550","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108550","url":null,"abstract":"The paper introduces an averaged model suitable for studying the long-term attitude dynamics of low Earth orbit objects subject to the interaction with the exosphere. This work extends previous results by the authors on the development of a semi-analytical theory for long-term attitude propagation. The first-order averaged model is developed by expressing the rotational problem in modified Sadov variables and performing the average of the equations of motion over the fast Sadov angles and the orbital mean anomaly. A transformation from osculating to mean variables is also derived from a combination of Lie transformations. The approach proposed in this paper is applied to two possible atmospheric drag models: a simple, commonly used, model characterised by a constant dimensionless drag coefficient and a higher fidelity model based on the theory by Sentman (1961).","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"192 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911853","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}
Pub Date : 2024-12-19DOI: 10.1016/j.cnsns.2024.108547
Lanmei Deng, Rong Hu, Ya-Ping Fang
We present an extragradient-type algorithm for solving a nonmonotone and non-Lipschitzian equilibrium problem over the fixed point set of a nonexpansive mapping in a Hilbert space. We obtain that the sequence generated by the presented algorithm converges weakly to a solution of the problem. The weak convergence does not require any monotonicity and Lipschitz continuity of the involved equilibrium function. This is a result of projecting the current point onto shrinking convex subsets of the feasible set at each iteration and employing an Armijo-type linesearch with subgradient. The numerical behavior has shown the efficiency of the proposed algorithm.
{"title":"An extragradient-type algorithm for solving a nonmonotone equilibrium problem over the fixed point set in a Hilbert space","authors":"Lanmei Deng, Rong Hu, Ya-Ping Fang","doi":"10.1016/j.cnsns.2024.108547","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108547","url":null,"abstract":"We present an extragradient-type algorithm for solving a nonmonotone and non-Lipschitzian equilibrium problem over the fixed point set of a nonexpansive mapping in a Hilbert space. We obtain that the sequence generated by the presented algorithm converges weakly to a solution of the problem. The weak convergence does not require any monotonicity and Lipschitz continuity of the involved equilibrium function. This is a result of projecting the current point onto shrinking convex subsets of the feasible set at each iteration and employing an Armijo-type linesearch with subgradient. The numerical behavior has shown the efficiency of the proposed algorithm.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"51 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886815","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}
Pub Date : 2024-12-19DOI: 10.1016/j.cnsns.2024.108536
Peng Miao, Huihui Huang
There are already several methods to calculate the time-varying minimal rank outer inverse (TV-MROI), but few scholars have employed fixed-time methods to obtain TV-MROI. To obtain TV-MROI within a fixed time frame, this paper introduces four novel fixed-time zeroing neural network (ZNN) models specifically designed to solve the TV-MROI problem. Compared with existing ZNN models, the proposed fixed-time ZNN model can attain TV-MROI before a fixed time, irrespective of the starting initial value. Initially, a new fixed-time stability criterion is established, utilizing a specialized Lyapunov function to ensure stability within a fixed period. Furthermore, a tighter upper bound for the convergence time is derived. An analysis of how various parameters affect this upper bound is undertaken, providing valuable insights into optimal parameter selection. Subsequently, the paper addresses both TV-MROI with specified range and kernel. To tackle these challenges, four innovative fixed-time zeroing neural network models are proposed, along with their respective fixed-time stability theorems. Finally, simulation results demonstrate the efficacy of our proposed methods.
{"title":"Novel fixed-time zeroing neural network models for solving time-varying minimal rank outer inverse problem","authors":"Peng Miao, Huihui Huang","doi":"10.1016/j.cnsns.2024.108536","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108536","url":null,"abstract":"There are already several methods to calculate the time-varying minimal rank outer inverse (TV-MROI), but few scholars have employed fixed-time methods to obtain TV-MROI. To obtain TV-MROI within a fixed time frame, this paper introduces four novel fixed-time zeroing neural network (ZNN) models specifically designed to solve the TV-MROI problem. Compared with existing ZNN models, the proposed fixed-time ZNN model can attain TV-MROI before a fixed time, irrespective of the starting initial value. Initially, a new fixed-time stability criterion is established, utilizing a specialized Lyapunov function to ensure stability within a fixed period. Furthermore, a tighter upper bound for the convergence time is derived. An analysis of how various parameters affect this upper bound is undertaken, providing valuable insights into optimal parameter selection. Subsequently, the paper addresses both TV-MROI with specified range and kernel. To tackle these challenges, four innovative fixed-time zeroing neural network models are proposed, along with their respective fixed-time stability theorems. Finally, simulation results demonstrate the efficacy of our proposed methods.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"32 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886865","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}
Pub Date : 2024-12-18DOI: 10.1016/j.cnsns.2024.108542
Luke Li, Qintao Gan, Ruihong Li, Qiaokun Kang, Huaiqin Wu
In this article, the fixed-/predefined-time stability (FXTS/PTS) problems of impulsive fuzzy neural networks are concerned. Under the framework of Filippov solution, some more comprehensive FXTS/PTS theorems of discontinuous impulsive systems are first established by employing the Lyapunov method. Compared to most existing results, which require the Lyapunov function (LF) to be negative or semi-negative definite, the unique novelty of the Lyapunov method lies in the derivative of the LF possessing indefiniteness. Besides, more general impulse effects with time-varying impulse strength are especially considered in this article. Then the obtained FXTS/PTS theorems are further utilized to deal with the FXTS/PTS problems of impulsive fuzzy neural networks by developing different control strategies. Two numerical simulations are proposed to illustrate the effectiveness of the achieved results.
{"title":"Fixed-/predefined-time stability of impulsive fuzzy neural networks: Lyapunov method with indefinite derivative","authors":"Luke Li, Qintao Gan, Ruihong Li, Qiaokun Kang, Huaiqin Wu","doi":"10.1016/j.cnsns.2024.108542","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108542","url":null,"abstract":"In this article, the fixed-/predefined-time stability (FXTS/PTS) problems of impulsive fuzzy neural networks are concerned. Under the framework of Filippov solution, some more comprehensive FXTS/PTS theorems of discontinuous impulsive systems are first established by employing the Lyapunov method. Compared to most existing results, which require the Lyapunov function (LF) to be negative or semi-negative definite, the unique novelty of the Lyapunov method lies in the derivative of the LF possessing indefiniteness. Besides, more general impulse effects with time-varying impulse strength are especially considered in this article. Then the obtained FXTS/PTS theorems are further utilized to deal with the FXTS/PTS problems of impulsive fuzzy neural networks by developing different control strategies. Two numerical simulations are proposed to illustrate the effectiveness of the achieved results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"48 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887056","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}
Pub Date : 2024-12-18DOI: 10.1016/j.cnsns.2024.108498
Elisa Maria Alessi, Inmaculada Baldomá, Mar Giralt, Marcel Guardia, Alexandre Pousse
Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability of the fixed points associated with the secular Hamiltonian averaged with respect to the fast variable with the corresponding periodic orbits of the full system. Focusing on the orbit of the Galileo satellites, it turns out that the two dynamics cannot be confused, as the relative difference depends on the ratio between the semi-major axis of Galileo and the one of the Moon, that is not negligible. The result is relevant to construct rigorously the Arnold diffusion mechanism that can drive a natural growth in eccentricity that allows a satellite initially on a circular orbit in Medium Earth Orbit to reenter into the Earth’s atmosphere.
{"title":"On the role of the fast oscillations in the secular dynamics of the lunar coplanar perturbation on Galileo satellites","authors":"Elisa Maria Alessi, Inmaculada Baldomá, Mar Giralt, Marcel Guardia, Alexandre Pousse","doi":"10.1016/j.cnsns.2024.108498","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108498","url":null,"abstract":"Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability of the fixed points associated with the secular Hamiltonian averaged with respect to the fast variable with the corresponding periodic orbits of the full system. Focusing on the orbit of the Galileo satellites, it turns out that the two dynamics cannot be confused, as the relative difference depends on the ratio between the semi-major axis of Galileo and the one of the Moon, that is not negligible. The result is relevant to construct rigorously the Arnold diffusion mechanism that can drive a natural growth in eccentricity that allows a satellite initially on a circular orbit in Medium Earth Orbit to reenter into the Earth’s atmosphere.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"1 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886868","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}
Pub Date : 2024-12-18DOI: 10.1016/j.cnsns.2024.108527
C. Chittam, S.V. Meleshko
This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive the general solution for the Maxwell model with the Johnson-Segalman convected derivative in cylindrical coordinates for an arbitrary model parameter α. The analysis reveals the necessity of separately considering the upper-convected, lower-convected, and Jaumann derivatives when solving the stagnation point flow problem.
{"title":"General solution of the Maxwell equations for the stagnation point problem with cylindrical symmetry for all values of the parameter in the Johnson-Segalman derivative","authors":"C. Chittam, S.V. Meleshko","doi":"10.1016/j.cnsns.2024.108527","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108527","url":null,"abstract":"This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive the general solution for the Maxwell model with the Johnson-Segalman convected derivative in cylindrical coordinates for an arbitrary model parameter <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>α</mml:mi></mml:math>. The analysis reveals the necessity of separately considering the upper-convected, lower-convected, and Jaumann derivatives when solving the stagnation point flow problem.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"4 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886867","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}
Pub Date : 2024-12-17DOI: 10.1016/j.cnsns.2024.108539
Hitalo Joseferson Batista Nascimento, Paulo Regis Menezes Sousa, José Leonardo Esteves da Silva
In this work the authors present a new class of radial basis functions (RBF) using functions from the κ-generalized Kaniadakis thermostatistics and the Lambert–Kaniadakis Wκ function, a recent generalization of the Lambert W function using the κ-exponential. Such functions are used to build neural networks of radial basis functions (RBFN). Two applications of these new RBFNs are described: In the first, we use such networks with κ=1/3 to train data that describe a time serie with additive noise. Second, we use the same RBFNs to numerically calculate the solution of Fredholm linear integral equations of the second kind.
{"title":"Radial basis function network using Lambert–Kaniadakis [formula omitted] function","authors":"Hitalo Joseferson Batista Nascimento, Paulo Regis Menezes Sousa, José Leonardo Esteves da Silva","doi":"10.1016/j.cnsns.2024.108539","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108539","url":null,"abstract":"In this work the authors present a new class of radial basis functions (RBF) using functions from the <mml:math altimg=\"si82.svg\" display=\"inline\"><mml:mi>κ</mml:mi></mml:math>-generalized Kaniadakis thermostatistics and the Lambert–Kaniadakis <mml:math altimg=\"si9.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>κ</mml:mi></mml:mrow></mml:msub></mml:math> function, a recent generalization of the Lambert <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mi>W</mml:mi></mml:math> function using the <mml:math altimg=\"si82.svg\" display=\"inline\"><mml:mi>κ</mml:mi></mml:math>-exponential. Such functions are used to build neural networks of radial basis functions (RBFN). Two applications of these new RBFNs are described: In the first, we use such networks with <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mrow><mml:mi>κ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> to train data that describe a time serie with additive noise. Second, we use the same RBFNs to numerically calculate the solution of Fredholm linear integral equations of the second kind.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"5 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886870","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}
The work is dedicated to exploring nonlinear modal interactions and mechanisms of energy transfer between a linear oscillator and a nonlinear energy sink in the gravitational field. Nonlinear modal interactions are studied based on the frequency-energy plot. Periodic motions are computed via numerical continuation method. Numerical evidences reveal that a 1:1 in-phase oscillation exists at low energies, and as energy increases, a 1:2 subharmonic tongue emerges from this 1:1 backbone branch. Besides, at high-energy levels, the NES engages in every n:m internal resonance with the LO. Differences on nonlinear modal interactions and energy transfer are compared between the cases of considering and neglecting effects of weights. Distinct nonlinear modal interactions depicted in the form of the frequency-energy plots are found at low-energy levels. For the case of the presence of weights, 1:1 transient resonance capture (TRC) or 1:2 subharmonic TRC governs nonlinear energy transfer. It means that energy transfer is still activated at low input energies, which perhaps breaks the limitation of critical energy threshold. The effects of NES parameters on frequency-energy relations for the underlying undamped system are also discussed via harmonic balance method. These discussions on nonlinear modal interactions and energy transfer provide a guidance for engineering application of the NES.
{"title":"Nonlinear modal interactions of a linear oscillator coupled to a cubic nonlinear oscillator in the gravitational field","authors":"Xiang Li, Wen-An Jiang, Xiujing Han, Qin-Sheng Bi, Li-Qun Chen","doi":"10.1016/j.cnsns.2024.108554","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108554","url":null,"abstract":"The work is dedicated to exploring nonlinear modal interactions and mechanisms of energy transfer between a linear oscillator and a nonlinear energy sink in the gravitational field. Nonlinear modal interactions are studied based on the frequency-energy plot. Periodic motions are computed via numerical continuation method. Numerical evidences reveal that a 1:1 in-phase oscillation exists at low energies, and as energy increases, a 1:2 subharmonic tongue emerges from this 1:1 backbone branch. Besides, at high-energy levels, the NES engages in every <ce:italic>n:m</ce:italic> internal resonance with the LO. Differences on nonlinear modal interactions and energy transfer are compared between the cases of considering and neglecting effects of weights. Distinct nonlinear modal interactions depicted in the form of the frequency-energy plots are found at low-energy levels. For the case of the presence of weights, 1:1 transient resonance capture (TRC) or 1:2 subharmonic TRC governs nonlinear energy transfer. It means that energy transfer is still activated at low input energies, which perhaps breaks the limitation of critical energy threshold. The effects of NES parameters on frequency-energy relations for the underlying undamped system are also discussed via harmonic balance method. These discussions on nonlinear modal interactions and energy transfer provide a guidance for engineering application of the NES.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"122 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886869","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}
Pub Date : 2024-12-17DOI: 10.1016/j.cnsns.2024.108533
Yue Zeng, Yao-jia Zhang, Nan-jing Huang
The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with Lévy jump (SFDVI with Lévy jump) under some mild conditions. We verify that Mosco convergence of the perturbed set implies point convergence of the projection onto the Hilbert space consisting of special stochastic processes whose range is the perturbed set. Moreover, by using the projection method and some inequality techniques, we establish a strong convergence result for the solution of SFDVI with Lévy jump when the mappings and constraint set are both perturbed. Finally, we apply the stability results to the spatial price equilibrium problem and the multi-agent optimization problem in stochastic environments.
本文的主要目的是研究在一些温和条件下，具有莱维跳跃的随机分数微分变分不等式（SFDVI with Lévy jump）的多参数稳定性结果。我们验证了扰动集的 Mosco 收敛性意味着投影到由特殊随机过程组成的希尔伯特空间的点收敛性，而特殊随机过程的范围就是扰动集。此外，通过使用投影方法和一些不等式技术，我们建立了当映射和约束集都受到扰动时，具有莱维跳跃的 SFDVI 解的强收敛结果。最后，我们将稳定性结果应用于随机环境中的空间价格均衡问题和多代理优化问题。
{"title":"Stability for a stochastic fractional differential variational inequality with Lévy jump","authors":"Yue Zeng, Yao-jia Zhang, Nan-jing Huang","doi":"10.1016/j.cnsns.2024.108533","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108533","url":null,"abstract":"The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with Lévy jump (SFDVI with Lévy jump) under some mild conditions. We verify that Mosco convergence of the perturbed set implies point convergence of the projection onto the Hilbert space consisting of special stochastic processes whose range is the perturbed set. Moreover, by using the projection method and some inequality techniques, we establish a strong convergence result for the solution of SFDVI with Lévy jump when the mappings and constraint set are both perturbed. Finally, we apply the stability results to the spatial price equilibrium problem and the multi-agent optimization problem in stochastic environments.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"114 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849247","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}
Pub Date : 2024-12-16DOI: 10.1016/j.cnsns.2024.108532
Zijia Peng, Guoqing Zhang, Stanisław Migórski
The paper is concerned with a new class of differential hemivariational inequalities which appears as the weak formulation of steady thermistor problems with mixed boundary conditions. First, we show the existence of solution to this kind of inequality problems combining the theory of pseudomonotone operators and a fixed point argument. Then, an optimal control problem is considered where the control is represented by the heat source. We introduce parameter perturbations of the electric conductivity and the boundary temperature in the system to examine their impact on the sensitivity properties of the optimal control problem. We prove that the optimal state-control set is nonempty and the value function of the optimal control problem is continuous. Finally, the multivalued map induced by optimal state-control set is established to be weakly upper semicontinuous in the weak topology.
{"title":"Sensitivity analysis of optimal control problems for differential hemivariational inequalities in steady thermistor problem","authors":"Zijia Peng, Guoqing Zhang, Stanisław Migórski","doi":"10.1016/j.cnsns.2024.108532","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108532","url":null,"abstract":"The paper is concerned with a new class of differential hemivariational inequalities which appears as the weak formulation of steady thermistor problems with mixed boundary conditions. First, we show the existence of solution to this kind of inequality problems combining the theory of pseudomonotone operators and a fixed point argument. Then, an optimal control problem is considered where the control is represented by the heat source. We introduce parameter perturbations of the electric conductivity and the boundary temperature in the system to examine their impact on the sensitivity properties of the optimal control problem. We prove that the optimal state-control set is nonempty and the value function of the optimal control problem is continuous. Finally, the multivalued map induced by optimal state-control set is established to be weakly upper semicontinuous in the weak topology.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"15 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886872","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}
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