In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the ...In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.展开更多
In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Ki...In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.展开更多
In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial m...In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.展开更多
The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method...The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method, obtain the equivalent norm in space , and we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectral interval condition.展开更多
Nowadays,inertial confinement fusion(ICF)research related to noncontact positioning and transport of free-standing cryogenic targets is playing an increasingly important role in this field.The operational principle be...Nowadays,inertial confinement fusion(ICF)research related to noncontact positioning and transport of free-standing cryogenic targets is playing an increasingly important role in this field.The operational principle behind these technologies is the magnetic acceleration of the levitating target carrier(or sabot)made from Type-Ⅱ,high-temperature superconductors(HTSCs).The physics of interaction among levitation,guidance and propulsion systems is based on a quantum levitation of high-pinning HTSCs in the mutually normal magnetic fields.This paper discusses current target delivery strategies and future perspectives to create different permanent magnet guideway(PMG)systems for ICF target transport with levitation.In particular,several PMG building options for optimizing both suspension and levitation of ICF targets using an HTSC-sabot will be analyzed.Credible solutions have been demonstrated for both linear and round PMGs,including the ones with a cyclotron acceleration process to realize high-running velocities of the HTSCsabot for a limited magnetic track.Focusing on physics,we describe in detail the main aspects of the PMG building and the results obtained from computations and proof of principle experiments.High-pinning HTSC magnetic levitation promises a stable and self-controlled levitation to accelerate the ICF targets placed in the HTSC-sabots up to the required injection velocities of 200 m/s and beyond.展开更多
Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to e...Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to enhance the speed of the convergence and reduce computational cost,the algorithms used a new step size and a cutting hyperplane.The first algorithm was proved to be weak convergence,while the second algorithm used a modified version of Halpern iteration to obtain strong convergence.Finally,numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.展开更多
基金Supported by the National Natural Science Foundation of China(72071130)。
文摘In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.
文摘In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.
文摘In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.
文摘The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method, obtain the equivalent norm in space , and we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectral interval condition.
基金Supported by NSFC(No.12171062)Natural Science Foundation of Chongqing Province(No.CSTB2022NSCQ-JQX0004)+2 种基金Science and Technology Project of Chongqing Education Committee(No.KJZDK201900504)Program of Chongqing Innovation Research Group Project in University(No.CXQT19018)Graduate Research Innovation Project of Chongqing(Nos.CYS21269,CYS22553)
基金the IAEA within project No.24154,‘Modeling of the Optics Degradation under Ionizing Radiation and Mass Fabrication of Low Aspect-Ratio Targets for a Repetition-Rate IFE Facility’the framework of the LPI State Task and under the program of the Presidium of the Russian Academy of Sciences。
文摘Nowadays,inertial confinement fusion(ICF)research related to noncontact positioning and transport of free-standing cryogenic targets is playing an increasingly important role in this field.The operational principle behind these technologies is the magnetic acceleration of the levitating target carrier(or sabot)made from Type-Ⅱ,high-temperature superconductors(HTSCs).The physics of interaction among levitation,guidance and propulsion systems is based on a quantum levitation of high-pinning HTSCs in the mutually normal magnetic fields.This paper discusses current target delivery strategies and future perspectives to create different permanent magnet guideway(PMG)systems for ICF target transport with levitation.In particular,several PMG building options for optimizing both suspension and levitation of ICF targets using an HTSC-sabot will be analyzed.Credible solutions have been demonstrated for both linear and round PMGs,including the ones with a cyclotron acceleration process to realize high-running velocities of the HTSCsabot for a limited magnetic track.Focusing on physics,we describe in detail the main aspects of the PMG building and the results obtained from computations and proof of principle experiments.High-pinning HTSC magnetic levitation promises a stable and self-controlled levitation to accelerate the ICF targets placed in the HTSC-sabots up to the required injection velocities of 200 m/s and beyond.
文摘Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to enhance the speed of the convergence and reduce computational cost,the algorithms used a new step size and a cutting hyperplane.The first algorithm was proved to be weak convergence,while the second algorithm used a modified version of Halpern iteration to obtain strong convergence.Finally,numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.
