发表的著作和论文部分

⑴对具mutualist的多种群反应扩散模型的研究（见Math. Biosci. 78 （1986），217--245; J. Math. Anal. Appl. 124 （1987），254-280; J. Partial Differential Equations 7 （1994），264--268）.是最早进行这类问题研究的学者之一，有较广泛的国际影响，有关文章被国内外同行广泛引用至今.⑵对具非均匀反应项的反应扩散方程解的渐近性的研究（见Proc. Amer. Math. Soc. 98 （1996），103--108.也见王明新的专著“非线性抛物方程”（科学出版社，1993））.⑶关于反应扩散方程组弱不变区域理论的研究（国家自然科学基金项目“反应扩散方程组弱不变区域的理论与数学生态学模型”，19371017），将不变区域的经典理论与Alikakos和Rothe最大模估计的技巧结合起来，引进了弱不变区域的新概念，并建立有界弱不变区域的判定定理.这一新的理论框架充分利用系统中各个分量之间的相互作用，允许反应项的适度增长性，可容纳相当广泛的（特别是具实际背景的）反应扩散方程组，从而将解的存在性的证明大大简化（见应用数学学报17 （1994），578--584; Proc. Roy. Soc. Edinburgh 130A （2000),1165-1180），得到多位国内外专家的肯定和好评.⑷关于反应扩散方程组中临界增长性的分析研究（国家自然科学基金项目“关于反应扩散方程组临界增长性的分析及其数值模拟”，19871008）.主要工作见 Math. Methods Appl. Sci. 22 （1999），43-54(SCI); J. Math. Anal. Appl. 232 （1999），293--311; Nonlinear Anal. 39 （2000),327--340.已引起国内外同行的注意，被多次引用. 得到著名数学家J. Serrin（美国科学院院士）的好评.⑸关于非线性双曲守恒律组广义解的稳定性和唯一性的研究（见 J. Math. Res. Exposition 5 （1985），89--93; Acta Math. Sci. 4 （1984），443--454; Proc. Amer. Math. Soc. 96 （1986），295-296），改进和推广了著名数学家R. DiPerna的重要工作，得到DiPerna本人的充分肯定.为美国“数学评论”（Mathematical Reviews）撰写这些领域的评论150余则. 以下为2000年前以本人为唯一作者的部分工作（限于列举被SCI检索的国外期刊文章）.Sining Zheng,A necessary condition for $L^2$ stability of quasilinear conservation laws,Proc. Amer. Math. Soc. 96 （1986），no. 3,495--496. (SCI)Sining Zheng,A reaction-diffusion system of a predator-prey-mutualist model,Math. Biosci. 78 （1986），no. 2,217--245. (SCI)Sining Zheng,A reaction-diffusion system of a competitor-competitor-mutualist model,J. Math. Anal. Appl. 124 （1987），no. 1,254--280. (SCI)Sining Zheng,A note on asymptotic behavior of solutions to a heterogeneous nonlinear reaction-diffusion system,Proc. Amer. Math. Soc. 98 （1986），no. 1,103--108. (SCI)Sining Zheng,Global boundedness of solutions to a reaction-diffusion system,Math. Methods Appl. Sci. 22 （1999），no. 1,43--54. (SCI)Sining Zheng,Nonexistence of positive solutions to a semilinear elliptic system and blow-up estimates for a reaction-diffusion system,J. Math. Anal. Appl. 232 （1999），no. 2,293--311.（SCI)Sining Zheng,Global existence and global non-existence of solutions to a reaction-diffusion system,Nonlinear Anal. 39 （2000),no. 3,Ser. A: Theory Methods,327--340. (SCI).Sining Zheng,Weakly invariant regions for reaction-diffusion systems and applications,Proc. Roy. Soc. Edinburgh Sect. A 130 （2000),no. 5,1165--1180. (SCI) 以下为2002年后与学生合作发表的部分文章（仅限于列举属于SCI检索的国外期刊文章.国家自然科学基金项目“多重非线性抛物方程组的临界指标与解的奇性传播”，10471013）:Sining Zheng,Lizhong Zhao andFeng Chen，Blow-up rates in a parabolic system of ignition model,Nonlinear Anal. 51 （2002），no. 4. 663--672.(SCI)Lizhong Zhao,Sining Zheng，Blow-up estimates for system of heat equations coupled via nonlinear boundary flux,Nonlinear Anal. 54 （2003），no. 2,251--259. (SCI)Xianfa Song,Sining Zheng,Blow-up and blow-up rate for a reaction-diffusion model with multiple nonlinearities,Nonlinear Anal. 54 （2003），no. 2,279--289.(SCI)Xianfa Song,Sining Zheng,Blow-up analysis for a quasilinear parabolic system with multi-coupled nonlinearities,J. Math. Anal. Appl. 281 （2003），no. 2,739--756.(SCI)Sining Zheng,Jing Liu,Coexistence solutions for a reaction–diffusion system of un-stirred chemostat model,Appl. Math. Comput. 145 （2003），no. 2-3,579--590.(SCI)Sining Zheng,Wenmiao Liang and Xianfa Song,Critical exponents in a parabolic system with inner absorption and coupled nonlinear boundary flux,Appl. Math. Comput. 154 （2004），no.2，567--581.(SCI)Zhaoxin Jiang,Sining Zheng and Xianfa Song,Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary condition,Appl. Math. Letters 17 （2004），193--199.(SCI)XianfaSong and Sining Zheng,Multi-nonlinear interactions in quasilinearreaction-diffusion equations with nonlinear boundary flux,Math. Comput. Modellng 39 （2004），133--144.(SCI)Sining Zheng,Xianfa Song and Zhaoxin Jiang,Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary conditions,J. Math. Anal. Appl. 298 （2004），308--324.(SCI)Lizhong Zhao,Sining Zheng,Critical exponents and asymptotic estimates of solutions to parabolic systems with localized nonlinear sources,J. Math. Anal. Appl. 292 （2004），621--635.(SCI)Sining Zheng,Xianfa Song,Interactions among multi-nonlinearities in a nonlinear diffusion system with absorptions and nonlinear boundary flux,Nonlinear Anal. 57 （2004），no.4,519--530.(SCI)Xianfa Song,Sining Zheng and Zhaoxin Jiang,Blow-up analysis for a nonlinear diffusion system,Z. Angew. Math. Phys. 56 （2005），1--10. (SCI)Sining Zheng,Fengjie Li,Critical exponents for a reaction-diffusion model with absorptions and coupled boundary flux,Proc. Edinburgh Math. Soc. 48 （2005），241--252. (SCI)Sining Zheng,Bingchen Liu and Fengjie Li,Blow-up rate estimates for a doubly coupled reaction-diffusion system,J. Math. Anal. Appl. 312 ⑵ （2005），576-595. (SCI)Sining Zheng,Bingchen Liu,A nonlinear diffusion system with convection,Nonlinear Anal. 63 （2005），123-135. (SCI)Chunpeng Wang,Sining Zheng,Critical Fujita exponents of degenerate and singular parabolic equations,Proc. Roy. Soc. Edinburgh A 136 （2006），415-430. (SCI)Sining Zheng,Bingchen Liu and Fengjie Li,Non-simultaneous blow-up for a multi-coupled reaction-diffusion system,Nonlinear Anal.64 ⑹ （2006），1189-1202. (SCI)Sining Zheng,Fengjie Li and Bingchen Liu,Asymptotic behavior for a reaction-diffusion equation with inner absorption and boundary flux,Appl. Math. Letters19 ⑼ （2006），942-948. (SCI)Peidong Lei,Sining Zheng,Global and non-global weak solutions to a degenerate parabolic system,J. Math. Anal. Appl. 324 ⑴ （2006），177-198. (SCI)Sining Zheng,Lan Qiao,Non-simultaneous blow-up in a reaction-diffusion system,Appl. Math. Compt. 180 ⑴ （2006），309--317. (SCI)Sining Zheng,Han Su,A Quasilinear reaction-diffusion system coupled via nonlocal sources,Appl. Math. Compt. 180 ⑴ （2006），295--308. (SCI)Sining Zheng,Wei Wang,Blow-up rate for a nonlinear diffusion equation,Appl. Math. Letters 19 ⑿ （2006），1385-1389. (SCI)Jing Liu,Sining Zheng,Second bifurcation for a food-chain model in an un-stirred chemostat,Differential Equations Dynam. Systems 14 （2006），225--238.Sining Zheng,Bingchen Liu and Fengjie Li,Simultaneous and non-simultaneous blow-up for a cross-coupled parabolic system,J. Math. Anal. Appl. 326 ⑴ （2007），414-431 . (SCI)Sining Zheng,Wei Wang,Critical exponents for a nonlinear diffusion system,Nonlinear Anal.,NA|5458,PⅡ： S0362-546X(06）00405-6,DOI information10.1016/j.na.2006.07.007，in press. Available online 17 August 2006. (SCI)Sining Zheng,Lidong Wang,Blow-up rate and profile for a degenerate parabolic system coupled via nonlocal sources,Compt. Math. Appl.,in press. (SCI)Fengjie Li,Sining Zheng and Bingchen Liu,Blow-up properties of solutions for a multi-coupled parabolic system,Nonlinear Anal.,NA|5690,PⅡ： S032-546X(06）00690-0,DOI information10.1016/j.na.2006.10.049,in press. Available online 8 December 2006.(SCI)Bo Liang,Sining Zheng,Exponential decay to a quantum hydrodynamic model for semiconductors,Nonlinear Anal. Real World Appl.,NONRWA469,PⅡ： S1468-1218(06）00136-2,DOI information 10.1016/j.nonrwa.2006.11.001,in press. Available online 18 December 2006.（SCI)Fengjie Li,Bingchen Liu and Sining Zheng,Simultaneous and non-simultaneous blow-up for heat equations with coupled nonlinear boundary fluxes,Z. Angew. Math. Phys.,in press.（SCI)Sining Zheng,Lan Qiao,Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux,Comm. Pure Appl. Anal.,in press.（SCI)Sining Zheng,Jinhuan Wang,Total versus single point blow-up in heat equations with coupled localized sources,Asymptot. Anal. 51 ⑵ （2007），133--156. (SCI)