In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family. 相似文献
Journal of Algebraic Combinatorics - APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in $${\mathbb Z}Q$$ with respect to the translation. In this paper, we show that... 相似文献
Near-infrared(NIR) fluorescent materials with high photoluminescent quantum yields(PLQYs) have wide application prospects. Therefore, we design and synthesize a D-A type NIR organic molecule, TPATHCNE, in which triphenylamine and thiophene are utilized as the donors and fumaronitrile is applied as the acceptor. We systematically investigate its molecular structure and photophysical property. TPATHCNE shows high Tgof 110℃ and Td of 385℃ and displays an aggregation-induced emission(AIE) property. A narrow optical bandgap of 1.65 eV is obtained. The non-doped film of TPATHCNE exhibits a high PLQY of 40.3% with an emission peak at 732 nm, which is among the best values of NIR emitters. When TPATHCNE is applied in organic light-emitting diode(OLED), the electroluminescent peak is located at 716 nm with a maximum external quantum efficiency of 0.83%. With the potential in cell imaging, the polystyrene maleic anhydride(PMSA) modified TPATHCNE nanoparticles(NPs) emit strong fluorescence when labeling HeLa cancer cells, suggesting that TPATHCNE can be used as a fluorescent carrier for specific staining or drug delivery for cellular imaging. TPATHCNE NPs fabricated by bovine serum protein(BSA) are cultivated with mononuclear yeast cells, and the intense intracellular red fluorescence indicates that it can be adopted as a specific stain for imaging. 相似文献
The hypochlorous acid (HCIO) was synthesized from seawater by the Pt/WO3 photocatalyst under visible-light irradiation. The effect of WO3 morphology and Pt loading on the performance of the composite photocatalyst for the production of HCIO has been studied in detail. The study found that among the series of materials, hollow WO3 microspheres with a diameter of about 3 μm loaded with 1.0 wt% Pt have the best HCIO production performance. Over it, 14.52 μM of HClO (1.24 mg/L of free chlorine) was accumulated in 0.5 M NaCl solution after 2 h of visible-light photoirradiation. What is more, the concentration of HClO can reach 4.34 μM (0.354 mg/L free chlorine) in natural seawater for 1 h using this Pt/WO3 photocatalyst. Under visible-light irradiation, the Pt/WO3 photocatalyst has a good broad-spectrum antibacterial activity and the activity of inhibiting marine fouling algae. The Pt/WO3 photocatalyst has high stability and reusability. All these characteristics are conducive to the application in the field of marine antifouling. Moreover, the photocatalytic reaction mechanism was evaluated by studying the photoelectrochemical properties of Pt/WO3/FTO. This research provides a new strategy for replacing the traditional electrolytic marine antifouling system with the visible-light-catalyzed HClO production system.