In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data ...In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].展开更多
基金supported by Hunan Provincial Natural Science Foundation of China(2016JJ2061)Scientific Research Fund of Hunan Provincial Education Department(15B102)+3 种基金China Postdoctoral Science Foundation(2013M532169,2014T70991)NNSF of China(11671101,11371367,11271118)the Construct Program of the Key Discipline in Hunan Province(201176)the aid program for Science and Technology Innovative Research Team in Higher Education Institutions of Hunan Province(2014207)
文摘In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].
文摘本文提出了一种基于圆边响应曲线的离焦估计新算法,实现了调焦参数的标定和望远物镜的自动调焦。建立了圆形边缘的灰度响应与离焦半径的关系模型,设计了圆四周离焦半径的双阈值均值滤波器,实现了模糊图像离焦半径的精确估计,降低了运动模糊和噪声的影响。根据离焦半径与调焦距离的线性关系,采用折线拟合方法,求解正焦调焦距离。然后,利用多个物距和正焦像距,优化求解测距调焦模型参数,实现了成像系统的自动调焦。仿真和实际实验验证了离焦半径估计算法的有效性和鲁棒性。标定后的自动调焦成像系统图像清晰,拍摄距离在43~52 m之间的物理分辨率接近理论值的一半,可分辨线宽优于0.354 mm.
