⑵ The asymptotic behavior of solutions of reaction-diffusion equations with non-uniform reaction terms is studied (see proc. Amir. mathmatics SOC.98 ( 1996)， 103- 108)。 See also Wang Mingxin's monograph Nonlinear Parabolic Equation (Science Press, 1993).
⑶ On the study of weak invariant region theory of reaction-diffusion equation (National Natural Science Foundation project "Weak invariant region theory of reaction-diffusion equation and mathematical ecological model", 1937 10 17), the classical invariant region theory is combined with the maximum norm estimation technology of Alikakos and Rothe, and the new concept of weak invariant region is introduced. And the judgment theorem of bounded weakly invariant regions is established. This new theoretical framework makes full use of the interaction between components in the system, allows the moderate growth of reaction terms, and can accommodate a wide range of reaction-diffusion equations (especially those with practical background), thus greatly simplifying the proof of the existence of solutions (see Journal of Applied Mathematics 17 (1994), 578-584; Go on. Roy. SOC。 Edinburgh 130a (2000),1165-1180) have been affirmed and praised by many experts at home and abroad.
⑷ Analysis and research on critical growth of reaction-diffusion equation (National Natural Science Foundation project "Analysis and numerical simulation of critical growth of reaction-diffusion equation", 1987 1008). See math. Methods appl sci.22 (1999) and 43-54(SCI) were the main tasks. Math J. Anal. Application 232 (1999), 293-311; Nonlinear analysis. 39 (2000), 327-340. It has attracted the attention of colleagues at home and abroad and has been cited many times. It was praised by the famous mathematician J. Serrin (academician of the American Academy of Sciences).
5. Study on the stability and uniqueness of generalized solutions of nonlinear hyperbolic conservation laws (see J. Math. Resolution no 5 (1985), pp. 89-93; Acta mathematics. Sci。 4 ( 1984),443 - 454; Go on. Amir. mathmatics SOC.96 (1986), 295-296), perfected and popularized the important work of the famous mathematician R. DiPerna, and was fully affirmed by DiPerna himself.
He has written more than 65,438+050 reviews in these fields for the American Mathematical Review. The following is part of my work before 2000 (limited to citing foreign journal articles retrieved by SCI).
Necessary conditions for the $ l 2 $ stability of quasilinear conservation laws. Amir. mathmatics Socialist 96 (1986), No.3,495-496. (SCI)
Reaction-diffusion system of a predator-prey-reciprocity model, mathematics. Biosci。 78 (1986), No.2,217-245. (SCI)
Zheng Sining, Reaction-Diffusion System of Competition-Competition-Reciprocity Model, Journal of Mathematics. Anal. ApplicationNo. 124 (1987),No. 1, 254-280. (SCI)
Zheng Sining, A Note on Asymptotic Behavior of Solutions for a Class of Non-homogeneous Nonlinear Reaction-diffusion Systems, China Science Press, 2003. Amir. mathmatics Socialist 98 (1986), No.65438 +0, 103-108. (SCI)
Global boundedness of solutions for a class of reaction-diffusion systems, mathematics. Methods Applied science. 22 (1999), No.65438+0,43-54. (SCI)
Zheng Sining, nonexistence of positive solutions for a class of semilinear elliptic systems and blow-up estimation of solutions for a class of reaction-diffusion systems, Journal of Mathematics. Anal. Application No.232 (1999), No.2,293-311. (SCI)
Global existence and global nonexistence of solutions for a class of reaction-diffusion systems, nonlinear analysis. 39 (2000), No.3, Compilation A: Theoretical Methods, 327-340. (SCI)。
Zheng Sining, Weak Invariant Region of Reaction-Diffusion System and Its Application, China. Roy. The Edinburgh Sect of Socialism. A 130 (2000) No.51165-1180. (SCI) The following are some articles published in cooperation with students after 2002 (only articles in foreign journals retrieved by SCI are listed. National Natural Science Foundation Project "Critical Exponent and Singular Propagation of Solutions of Multiple Nonlinear Parabolic Equations", 6438+0047655.
Zheng Sining, Zhao Lizhonghe, blasting rate of parabolic system in ignition model, nonlinear analysis. 5 1 (2002) No.4. 663 - 672.(SCI)
Zhao Lizhong, Zheng Sining, Blow-up estimation and nonlinear analysis of heat equations coupled by nonlinear boundary flow. 54 (2003) No.2,251-259. (SCI)
Song, Zheng Sining, blow-up and blow-up rate of a reaction-diffusion model with multiple nonlinear terms, nonlinear analysis. 54 (2003), No.2,279-289. (SCI)
Song, Zheng Sining, Blow-up Analysis of Quasilinear Parabolic Systems with Multiple Coupled Nonlinear Terms, Journal of Mathematics. Anal. Application No.28 1 (2003)No. 2739-756. (SCI)
Zheng Sining, Co-existence Solution of Reaction-Diffusion System with Stirred Chemostat Model, Applied Mathematics. Computer. 145 (2003), No.2-3,579-590. (SCI)
Zheng Xinning, Liang, Song, Critical Exponent of Parabolic System with Internal Absorption and Coupled Nonlinear Boundary Flow, Applied Mathematics. Computer. 154 (2004) No.2 567-58 1. (SCI)
Jiang, Zheng Sining, Song, Blow-up analysis of a class of nonlinear diffusion equations under nonlinear boundary conditions, applied mathematics. Letter 17 (2004), 193-199. (SCI)
Song, Zheng Sining, Multiple nonlinear interactions in quasilinear reaction-diffusion equation with nonlinear boundary flow, mathematics. Computer. Model 39 (2004), 133-144. (SCI)
Zheng Sining, Song, Jiang, Critical Fujita exponent of degenerate parabolic equation coupled by nonlinear boundary conditions, Journal of Mathematics. Anal. Page 298 (2004), pages 308-324. (SCI)
Zhao Lizhong, Zheng Sining, Critical Exponent and Asymptotic Estimation of Solutions of Parabolic Systems with Local Nonlinear Sources, Journal of Mathematics. Anal. Application No.292 (2004), 62 1-635. (SCI)
Zheng Xinning, Song, Interaction and nonlinear analysis of multiple nonlinear terms in a nonlinear diffusion system with absorption and nonlinear boundary flux. 57 (2004) No.45 19-530. (SCI)
Song, Zheng Sining, Jiang, Blow-up Analysis of a Class of Nonlinear Diffusion Systems. mathmatics Phys. 56 (2005)， 1 - 10。 (SCI)
Critical exponent of reaction-diffusion model with absorbing and coupling boundary flow. Edinburgh mathematics. Socialist 48 (2005),24 1-252.(SCI)
Zheng Sining, Liu Fengjie, estimation of blasting rate of double-coupled reaction-diffusion system, journal of mathematics Anal. (2005) No.3 12, pp. 576-595. (SCI)
Zheng Sining, Liu, nonlinear diffusion system with convection, nonlinear analysis. 63 (2005), 123- 135.(SCI)
Wang, Zheng Sining, Critical Fujita Index of Degenerate and Singular Parabolic Equations, Journal of China Academy of Sciences. Roy. Socialist Edinburgh A 136 (2006), 4 15-430. (SCI)
Zheng Sining, Liu Fengjie, non-simultaneous blasting of multi-coupled reaction-diffusion system, nonlinear analysis. 64 ⑹ (2006), 1 189- 1202.(SCI)
Zheng Sining, Li Fengjie, Liu, Asymptotic behavior of reaction-diffusion equation with internal absorption and boundary flux, applied mathematics. Levies (2006), 942-948. (SCI)
Lei, Zheng Sining, Global and Nonglobal Weak Solutions of Degenerate Parabolic Systems, Journal of Mathematics. Anal. No.324 (2006), 177- 198. (SCI)
Zheng Sining, Blue Bridge, Non-simultaneous Blasting of Reaction-Diffusion System, Applied Mathematics. Compt。 180 ⑴ (2006),309 - 3 17.(SCI)
Zheng Sining, Quasi-linear Reaction-Diffusion System Coupled by Nonlocal Sources, Applied Mathematics. Compt。 180 ⑴ (2006),295 - 308.(SCI)
Zheng Sining, Blow-up Rate of a Class of Nonlinear Diffusion Equations, Applied Mathematics. ⑿(2006) 19, 1385- 1389. (SCI)
The second branch of the food chain model in the agitator-free chemostat, differential equation dynamics. System 14 (2006), 225-238.
Zheng Sining, Li Fengjie, simultaneous and non-simultaneous blasting of a class of cross-coupled parabolic systems, Journal of Mathematics. Anal. Application 326 (1) (2007), 4 14-43 1. (SCI)
Zheng Xinning, Critical Exponent of Nonlinear Diffusion System, Nonlinear Analysis. , NA|5458, Pⅱ:s 0362-546 x(06)00405-6, DOI information10.16/j.na.2006.07.007, in print. Available online on August 7, 2006 17. (SCI)
Zheng Sining, Wang Lidong, Blasting rate and profile of degenerate parabolic system coupled by nonlocal sources. mathmatics Application, in printing. (SCI)
Li Fengjie, Zheng Sining, Liu, Blow-up properties of solutions of multi-coupled parabolic equations, nonlinear analysis. , NA|5690, Pⅱ:S032-546 x(06)00690-0, DOI information1016/j.na.2006.10.049. 200618 February online. (SCI)
Exponential attenuation and nonlinear analysis of semiconductor quantum hydrodynamic model. Real-world application, NONRWA469, p Ⅱ: s1468-1218 (06) 00136-2, DOI information10. (SCI)
Li Fengjie, Zheng Sining, Simultaneous and Non-simultaneous Blow-up of Heat Equation with Coupled Nonlinear Boundary Fluxes, Zhang Zhiwei. mathmatics Physics, in publication. (SCI)
Zheng Sining, blue bridge, non-simultaneous blow-up of thermal equation with positive and negative sources and coupled boundary flow, general pure application analysis. , is being printed. (SCI)
Zheng Xinning, Global Blow-up of Thermal Equation with Coupled Local Sources and single point blowup, Asymptote. Anal. 5 1 ⑵ (2007), 133 - 156.(SCI)