In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, wher...In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.展开更多
The radar cross section （RCS） of weak scattering source on the surface of an aircraft is usually less than -40 dBsm. How to accurately measure the RCS characteristics of weak scattering source is a technical challen...The radar cross section （RCS） of weak scattering source on the surface of an aircraft is usually less than -40 dBsm. How to accurately measure the RCS characteristics of weak scattering source is a technical challenge for the aircraft＇s RCS measurement. This paper proposes separating and extracting the two-dimensional （2D） reflectivity distribution of the weak scattering source with the microwave imaging algorithm and spectral transform so as to enhance its measurement preci- sion. Firstly, we performed the 2D microwave imaging of the target and then used the 2D gating function to separate and extract the reflectivity distribution of the weak scattering source. Secondly, we carried out the spectral transform of the reflectivity distribution and eventually obtained the RCS of the weak scattering source through calibration. The prototype experimental results and their analysis show that the measurement method is effective. The experiments on an aircraft＇s low-scattering conformal antenna verify that the measurement method can eliminate the clutter on the surface of aircraft. The precision of measuring a -40 dBsm target is 3 5 dB better than the existing RCS measurement methods. The measurement method can more accurately obtain the weak scattering source＇s RCS characteristics.展开更多
文摘In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.
基金co-supported by the National Natural Science Foundation of China(Nos.61201320,61371023)the Fundamental Research Funds for the Central Universities of China(No.3102014JCQ01103)
文摘The radar cross section （RCS） of weak scattering source on the surface of an aircraft is usually less than -40 dBsm. How to accurately measure the RCS characteristics of weak scattering source is a technical challenge for the aircraft＇s RCS measurement. This paper proposes separating and extracting the two-dimensional （2D） reflectivity distribution of the weak scattering source with the microwave imaging algorithm and spectral transform so as to enhance its measurement preci- sion. Firstly, we performed the 2D microwave imaging of the target and then used the 2D gating function to separate and extract the reflectivity distribution of the weak scattering source. Secondly, we carried out the spectral transform of the reflectivity distribution and eventually obtained the RCS of the weak scattering source through calibration. The prototype experimental results and their analysis show that the measurement method is effective. The experiments on an aircraft＇s low-scattering conformal antenna verify that the measurement method can eliminate the clutter on the surface of aircraft. The precision of measuring a -40 dBsm target is 3 5 dB better than the existing RCS measurement methods. The measurement method can more accurately obtain the weak scattering source＇s RCS characteristics.
