This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the ...This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the weight functions, local terms and localized source on the blow-up properties. We will show that the weight functions play the substantial roles in determining whether the solutions will blow-up or not, and obtain the blow-up conditions and its blow-up rate estimate.展开更多
To investigate photoelectric properties of meso-extended porphyrin derivatives with electron-donating or elec- tron-withdrawing substituents, a series of functionalized porphyrin materials have been designed and synth...To investigate photoelectric properties of meso-extended porphyrin derivatives with electron-donating or elec- tron-withdrawing substituents, a series of functionalized porphyrin materials have been designed and synthesized by Suzuki coupling reaction. The meso-extended structures were fully characterized by IH NMR, IR spectroscopy and mass spectrometry. The photophysical properties of porphyrin derivatives were carefully examined by UV-Visible and fluorescence spectra, and the solvatochromic effect was observed and discussed. In particular, Z-scan technique was employed to characterize the third-order nonlinear optical （NLO） properties of the products such as nonlinear absorption and refraction, the third-order nonlinear refractive indexes （x（3）-value） of these porphyrin derivatives achieved 3.9 × 10-12 esu. In addition, the compounds could be self-assembled into highly organized morphologies through phase-exchange method. All the results indicated that the discotic materials have the potential for optoelec- tronic applications.展开更多
We are concerned with the Cauchy problem of the new integrable three-component system with cubic nonlinearity. We establish the local well- posedness in a range of the Besov spaces. Then the precise blow-up scenario f...We are concerned with the Cauchy problem of the new integrable three-component system with cubic nonlinearity. We establish the local well- posedness in a range of the Besov spaces. Then the precise blow-up scenario for strong solutions to the system is derived.展开更多
基金Acknowledgements This work was partially supported by the National Natural Science Foundation of China （Grant No. 11071266）, the Scholarship Award for Excellent Doctoral Student （Ministry of Education）, and the Foundation Project of China Yangtze Normal University （2011CJSKY012）.
文摘This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the weight functions, local terms and localized source on the blow-up properties. We will show that the weight functions play the substantial roles in determining whether the solutions will blow-up or not, and obtain the blow-up conditions and its blow-up rate estimate.
文摘To investigate photoelectric properties of meso-extended porphyrin derivatives with electron-donating or elec- tron-withdrawing substituents, a series of functionalized porphyrin materials have been designed and synthesized by Suzuki coupling reaction. The meso-extended structures were fully characterized by IH NMR, IR spectroscopy and mass spectrometry. The photophysical properties of porphyrin derivatives were carefully examined by UV-Visible and fluorescence spectra, and the solvatochromic effect was observed and discussed. In particular, Z-scan technique was employed to characterize the third-order nonlinear optical （NLO） properties of the products such as nonlinear absorption and refraction, the third-order nonlinear refractive indexes （x（3）-value） of these porphyrin derivatives achieved 3.9 × 10-12 esu. In addition, the compounds could be self-assembled into highly organized morphologies through phase-exchange method. All the results indicated that the discotic materials have the potential for optoelec- tronic applications.
基金Acknowledgements This work was partially supported by the National Natural Science Foundation of China （Grant No. 11371384）, the Natural Science Foundation of Chongqing （cstc2013jcyjA0940）, and the Natural Science Foundation of Fuling （FLKJ, 2013ABA2036）.
文摘We are concerned with the Cauchy problem of the new integrable three-component system with cubic nonlinearity. We establish the local well- posedness in a range of the Besov spaces. Then the precise blow-up scenario for strong solutions to the system is derived.
