In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the H...A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the Hawking temperature.Motivated by this,we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction.Numerically,we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field.They are mainly contributed by the bound states near the horizon and lie below the chaos bound.展开更多
We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-orde...We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-order convection term.By employing innovative integralbased test functions,we derive the necessary a priori estimates.To prove the convergence of solutions to the degenerate coercivity problem,we adopt a method that combines monotonicity and truncation techniques.This approach allows us to demonstrate that the gradient sequences converge almost everywhere.展开更多
In this paper,the authors establish the boundedness of Hardy-Littlewood maximal operators M^(ψ)associated withψ-rectangles on weighted Lebesgue spaces and on two kinds of Lorentz spaces with variable exponent,as wel...In this paper,the authors establish the boundedness of Hardy-Littlewood maximal operators M^(ψ)associated withψ-rectangles on weighted Lebesgue spaces and on two kinds of Lorentz spaces with variable exponent,as well as its corresponding Fefferman-Stein inequalities.All of these generalize the corresponding results in classical case.展开更多
We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
跟-构网型(grid following and grid-forming,GFL-GFM)变流器混合并网系统中多类型控制策略及控制切换行为使电压响应特性复杂多变,难以快速、准确评估其暂态电压稳定状态。为此,该文提出一种基于切换系统最大李雅普诺夫指数(switching ...跟-构网型(grid following and grid-forming,GFL-GFM)变流器混合并网系统中多类型控制策略及控制切换行为使电压响应特性复杂多变,难以快速、准确评估其暂态电压稳定状态。为此,该文提出一种基于切换系统最大李雅普诺夫指数(switching system maximum Lyapunov exponent,SSMLE)的跟-构网型变流器混合并网系统暂态电压稳定评估方法。首先,计及系统多运行状态和运行参数对暂态电压响应特性影响,建立混合并网系统不同运行工况下电压轨线变分方程;然后,在各运行状态下通过变分方程分段求解SSMLE,并采用切换补偿矩阵修正控制切换时刻积分终值矩阵偏差,提升电压稳定状态判别速度和准确度;其次,利用SSMLE分析系统关键参数对暂态电压稳定性的影响并确定暂态电压稳定参数域,可为调度人员获取系统运行状态、更新电压稳控策略提供参考;最后,通过GFL-GFM变流器混合并网系统和多机硬件在环仿真系统的仿真分析,验证所提方法的准确性和有效性。展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金supported by the National Natural Science Foundation of China with Grants No.12174067 and No.11804223。
文摘A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the Hawking temperature.Motivated by this,we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction.Numerically,we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field.They are mainly contributed by the bound states near the horizon and lie below the chaos bound.
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)。
文摘We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-order convection term.By employing innovative integralbased test functions,we derive the necessary a priori estimates.To prove the convergence of solutions to the degenerate coercivity problem,we adopt a method that combines monotonicity and truncation techniques.This approach allows us to demonstrate that the gradient sequences converge almost everywhere.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12471090,12201098)the Fundamental Research Funds for the Central Universities(Grant No.3132024199).
文摘In this paper,the authors establish the boundedness of Hardy-Littlewood maximal operators M^(ψ)associated withψ-rectangles on weighted Lebesgue spaces and on two kinds of Lorentz spaces with variable exponent,as well as its corresponding Fefferman-Stein inequalities.All of these generalize the corresponding results in classical case.
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
文摘跟-构网型(grid following and grid-forming,GFL-GFM)变流器混合并网系统中多类型控制策略及控制切换行为使电压响应特性复杂多变,难以快速、准确评估其暂态电压稳定状态。为此,该文提出一种基于切换系统最大李雅普诺夫指数(switching system maximum Lyapunov exponent,SSMLE)的跟-构网型变流器混合并网系统暂态电压稳定评估方法。首先,计及系统多运行状态和运行参数对暂态电压响应特性影响,建立混合并网系统不同运行工况下电压轨线变分方程;然后,在各运行状态下通过变分方程分段求解SSMLE,并采用切换补偿矩阵修正控制切换时刻积分终值矩阵偏差,提升电压稳定状态判别速度和准确度;其次,利用SSMLE分析系统关键参数对暂态电压稳定性的影响并确定暂态电压稳定参数域,可为调度人员获取系统运行状态、更新电压稳控策略提供参考;最后,通过GFL-GFM变流器混合并网系统和多机硬件在环仿真系统的仿真分析,验证所提方法的准确性和有效性。
