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| 1 | Propagations of singularities in a parabolic system with coupling nonlocal sources显示文摘This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also. | ZHANG He KONG LingHua ZHENG SiNing | 2009 | Science China Mathematics2009，52，1： | 10 |
| 2 | Fujita phenomena in nonlinear pseudo-parabolic system显示文摘This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut-△u-αut=vp,vt-△v-αvt=uqwith p,q 1 and pq>1,where the viscous terms of third order are included.We first find the critical Fujita exponent,and then determine the second critical exponent to characterize the critical space-decay rate of initial data in the co-existence region of global and non-global solutions.Moreover,time-decay profiles are obtained for the global solutions.It can be found that,diferent from those for the situations of general semilinear heat systems,we have to use distinctive techniques to treat the influence from the viscous terms of the highest order.To fix the non-global solutions,we exploit the test function method,instead of the general Kaplan method for heat systems.To obtain the global solutions,we apply the Lp-Lq technique to establish some uniform Lmtime-decay estimates.In particular,under a suitable classification for the nonlinear parameters and the initial data,various Lmtime-decay estimates in the procedure enable us to arrive at the time-decay profiles of solutions to the system.It is mentioned that the general scaling method for parabolic problems relies heavily on regularizing efect to establish the compactness of approximating solutions,which cannot be directly realized here due to absence of the smooth efect in the pseudo-parabolic system. | YANG JinGe CAO Yang ZHENG SiNing | 2014 | Science China Mathematics2014，57，3： | 5 |
| 3 | Asymptotic behavior for a reaction-diffusion equation with inner absorption and boundary flux显示文摘 | ZHENG Sining LI Fengjie LIU Bingchen | 2006 | Applied Mathematics Letters2006，19，： | 1 |
| 4 | The critical Fujita exponent for the fast diffusion equation with potential 显示文摘 | YANG Chunxiao ZHAO Lizhong ZHENG Sining | 2013 | J Math Anal2013，398，2： | 1 |
| 5 | Critical Exponent for Parabolic System with Time-Weighted Sources in Bounded Domain显示文摘 | BAI Xueli ZHENG Sining WANG Wei | 2013 | Journal of Functional Analysis2013，265，6： | 1 |
| 6 | Second critical exponent for a higher-order semilinear parabolic system显示文摘This paper studies a higher-order semilinear parabolic system. We obtain the second critical exponent to characterize the critical space-decay rate of the initial data in the co-existence parameter region of global and non-global solutions. Together with the critical Fujita exponent established by Pang et al.(2006),this gives a clear and complete picture to the Fujita phenomena in the coupled higher-order semilinear parabolic system. | YANG ChunXiao YANG JinGe ZHENG SiNing | 2015 | Science China Mathematics2015，58，7： | 1 |
| 7 | Blow-up rates in a parabolic system of ignition model显示文摘 | Sining Zheng Lizhong Zhao Feng Chen | 2002 | Nonlinear Analysis2002，，4： | 1 |
| 8 | Blow- up rate and profile for a degenerate parabolic system coupled via nonlocal sources显示文摘 | ZHENG Sining WANG Lidong | 2006 | Comput Math Appl2006，52，： | 1 |
| 9 | A semilinear parabolic system with coupling variable exponents显示文摘 | Xueli Bai and Sining Zheng | 2011 | Annali di Mathematic Pura ed Application2011，190，3： | 1 |
| 10 | Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions显示文摘 | Jiang Zhaoxin Zheng Sining Song Xianfa | 2004 | Applied Mathematics Letters2004，17，： | 1 |
| 11 | Blow-up and blow up rate for a reacton-diffusion model with multiple nonlinearities显示文摘 | Song Xianfa Zheng Sining | 2003 | Nonlinear Analysis2003，54，： | 1 |
| 12 | Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions显示文摘 | Zhaoxin Jiang Sining Zheng Xianfa Song | 2004 | Applied Mathematics Letters2004，，2： | 1 |
| 13 | Determination of Residual Amount of 15 Plant Growth Regulators in Bean Sprouts by HPLC-MS/MS显示文摘[Objectives]This study was conducted to effectively monitor PGR residues in bean sprouts to provide guarantee for the food safety of agricultural products.[Methods]A high-performance liquid chromatography-tandem mass spectrometry(HPLC-MS/MS)method for the determination of residues of 15 plant growth regulators(PGRs)in bean sprouts was established using bean sprouts as an experimental material.Samples were extracted with a solution containing 5%acetic acid-acetonitrile(1∶99,V/V),purified with anhydrous magnesium sulfate,and diluted with methanol solvent to constant volume.The solutions were filtered through 0.22μm filtering membrane and the target analytes were separated on a Phenomenex H18 column.The identification of each compound was established by retention time matching along with the accurate mass measurement of the precursor ions and their main fragment ions.The quantification was carried out using matrix-matched external standard method.[Results]The retention time of the 15 PGRs were found in the range from 5.8-11.7 min under the optimized conditions.The linear relation was good in the concentration range of 0.005-0.050μg/ml,and the correlation coefficients of the 15 PGRs were≥0.9990.The limits of detection were in the range of 0.03-0.92 g/kg,and the limits of quantification were in the range of 0.50-2.10μg/kg.The average recovery in the recovery test at 3 concentration levels was 80%-110%,and the relative standard deviations were in the range of 2.8%-7.5%.[Conclusions]This method is simple and accurate,and can quickly qualitatively and quantitatively analyze the residues of 15 PGRs in bean sprouts.The proposed procedure was simple,quick and accurate for the simultaneous determination of the 15 PGRs in bean sprout. | Lei WANG Yi ZHANG Baiqin ZHENG Shuai WANG Kai GE Sining TANG Shuhong ZHANG Liwu HAO | 2021 | Agricultural Biotechnology2021，10，6： | 1 |
| 14 | Global boundedness of solutions to a reaction-diffusion system显示文摘 | ZHENG Sining | | 0，，： | 1 |
| 15 | Global existence global non-existence of solutions to a reaction-diffusion system显示文摘 | ZHENG Sining | | 0，，： | 1 |
| 16 | Nonexistence of positive solutions to a semilinear elliptic system and blow-up estimates for a Reaction-Diffusion system显示文摘 | | 1999 | J Math Anal Appl1999，232，： | 1 |
| 17 | Critical exponents for a reaction-diffusion model with absorptions and coupled boundary flux显示文摘 | ZHENG Sining LI Fengjie | 2005 | Proc Edinb Math Soc2005，48，： | 1 |
| 18 | Global existence and global non-existence of solutions to a reaction-diffusion system显示文摘 | Sining ZHENG | | 0，，03： | 1 |
| 19 | Total versus single point blow-up in heat equations with coupled local zed sources显示文摘 | Sining ZHENG Jinhuan WANG | | 0，，02： | 1 |
| 20 | Simultaneous and non-simultaneous blow-up for a cross-coupled parabolic system显示文摘 | Sining ZHENG Bingchen LIU Fengjie LI | | 0，，01： | 1 |
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