In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we i...In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.展开更多
In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some dec...In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.展开更多
An isotropic electromagnetic （EM） lens based on Huygens＇ metasurface is proposed for 28.0 GHz lens antenna design. The lens consists of a series of non-resonant and subwavelength metallic patterns etched on both si...An isotropic electromagnetic （EM） lens based on Huygens＇ metasurface is proposed for 28.0 GHz lens antenna design. The lens consists of a series of non-resonant and subwavelength metallic patterns etched on both sides of an ultrathin dielectric substrate. Both electric and magnetic responses are introduced to realize desired abrupt phase change and high-efficiency transmission for the secondary wavelets in the incident wavefront. Then, a substrate-integrated waveguide （SIW） fed patch antenna is combined with the lens as the primary feed to form a low-profile lens antenna system. The simulated and measured results coincide with each other, and demonstrate that the prototype realizes 8.8 dB-12.6 dB gain increment and low side-lobe levels over the bandwidth of 26.7 GHz-30.0 GHz. The novel design leads to a low-profile, light weight, and low-cost antenna solution in a wireless communication system.展开更多
基金supported by National Science Foundation of China(11071162)Shanghai Municipal Natural Science Foundation (09ZR1413500)
文摘In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.
基金Xingwen Hao's research was supported in part by National Natural Science Foundation of China (10571120 and 10971135)Shanghai Shuguang Project (06SG11)+1 种基金the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) Doctorial Foundation of Weifang University (2011BS11)
文摘In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.
基金supported by the National Natural Science Foundation of China (61401229)the Science and Technology Project of Jiangsu Province (BE2015002-2)+1 种基金the Open Research Program of the State Key Laboratory of Millimeter Waves (K201616)the Nanjing University of Posts and Telecommunications Scientific Foundation (NY215137)
文摘An isotropic electromagnetic （EM） lens based on Huygens＇ metasurface is proposed for 28.0 GHz lens antenna design. The lens consists of a series of non-resonant and subwavelength metallic patterns etched on both sides of an ultrathin dielectric substrate. Both electric and magnetic responses are introduced to realize desired abrupt phase change and high-efficiency transmission for the secondary wavelets in the incident wavefront. Then, a substrate-integrated waveguide （SIW） fed patch antenna is combined with the lens as the primary feed to form a low-profile lens antenna system. The simulated and measured results coincide with each other, and demonstrate that the prototype realizes 8.8 dB-12.6 dB gain increment and low side-lobe levels over the bandwidth of 26.7 GHz-30.0 GHz. The novel design leads to a low-profile, light weight, and low-cost antenna solution in a wireless communication system.
