The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p...The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.展开更多
Ultrashort pulses complicate the frequency conversion in a nonlinear crystal, where group velocity mismatch becomes the main obstacle due to dispersion. We present a design for group velocity compensated second harmon...Ultrashort pulses complicate the frequency conversion in a nonlinear crystal, where group velocity mismatch becomes the main obstacle due to dispersion. We present a design for group velocity compensated second harmonic generation in a modulated nonlinear structure, embedded in a liquid crystal box. In this structure, nonlinear crystals act as sources of signal and liquid crystals compensate for group velocity mismatch originating from nonlinear crystals. There are the advantages of the flexible, controllable birefringence of liquid crystals. Meanwhile, a method calculating the parameters of this type of structure is presented. To make it clear, an example is provided. Furthermore, the structure can also be shaped as a waveguide to support integration into other optical devices, applicable to all-optical processing systems.展开更多
基金Yachun Li’s research was supported partly by National Natural Science Foundation of China (10571120,10971135)the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546)+3 种基金Shanghai Shuguang Project 06SG11Zhigang Wang’s research was supported partly by Shanghai Jiao Tong University Innovation Fund For Postgraduates (AE071202)the University Young Teacher Sciences Foundation of Anhui Province (2010SQRL145)the Quality Project Found of Fuyang Normal College (2010JPKC07)
文摘The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
基金Supported by the Natural Science Foundation of Heilongjiang Province under Grant Nos F201312,F2016023 and QC2015086the National Natural Science Foundation of China under Grant No 61405049
文摘Ultrashort pulses complicate the frequency conversion in a nonlinear crystal, where group velocity mismatch becomes the main obstacle due to dispersion. We present a design for group velocity compensated second harmonic generation in a modulated nonlinear structure, embedded in a liquid crystal box. In this structure, nonlinear crystals act as sources of signal and liquid crystals compensate for group velocity mismatch originating from nonlinear crystals. There are the advantages of the flexible, controllable birefringence of liquid crystals. Meanwhile, a method calculating the parameters of this type of structure is presented. To make it clear, an example is provided. Furthermore, the structure can also be shaped as a waveguide to support integration into other optical devices, applicable to all-optical processing systems.
