鄭斯寧

鄭斯寧教授,1946年11月生於重慶,祖籍河南羅山。

基本信息

主要學歷及工作經歷

1946年11月生於重慶,祖籍河南羅山。
1970年畢業於北京大學數學力學系。
在吉林大學數學系獲理學碩士(1981)和博士(1998)學位。導師伍卓群教授。
1981年起在大連理工大學套用數學系任教,先後任講師(1983), 副教授(1987),教授(1991),系主任(1998--2002)。
美國密西根大學(University of Michigan)數學系訪問學者(1984--85),美國加州理工學院(California Institute of Technology)套用數學系Visiting Associate (1995--96)。

主要學術及社會兼職

美國數學會會員(1986-),美國“數學評論”(Mathematical Reviews)評論員(1987-)

研究領域(研究課題)

非線性偏微分方程的理論和套用。非線性科學是當代科學最具挑戰性的關鍵性領域之一,而關於非線性偏微分方程的研究又是非線性科學的核心,其極端複雜性和多樣性直接反映了自然界現象(包括生命現象)的極端複雜性和多樣性。本人主要研究領域集中於非線性發展方程,特別是具有廣泛實際背景的非線性拋物方程(組),以及非線性雙曲守恆律組等。

指導碩、博士生研究方向

非線性偏微分方程的理論與套用。重點是對具有廣泛實際背景的非線性拋物方程(組)的研究,例如:複雜拋物系統中多重非線性之間的相互作用,解的奇性的產生與傳播等問題。

出版著作和論文

主要著作及論文

⑴對具mutualist的多種群反應擴散模型的研究(見Math. Biosci. 78 (1986),217--245; J. Math. Anal. Appl. 124 (1987),254-280; J. Partial Differential Equations 7 (1994),264--268).是最早進行這類問題研究的學者之一,有較廣泛的國際影響,有關文章被國內外同行廣泛引用至今.
⑵對具非均勻反應項的反應擴散方程解的漸近性的研究(見Proc. Amer. Math. Soc. 98 (1996),103--108.也見王明新的專著“非線性拋物方程”(科學出版社,1993)).
⑶關於反應擴散方程組弱不變區域理論的研究(國家自然科學基金項目“反應擴散方程組弱不變區域的理論與數學生態學模型”,19371017),將不變區域的經典理論與Alikakos和Rothe最大模估計的技巧結合起來,引進了弱不變區域的新概念,並建立有界弱不變區域的判定定理.這一新的理論框架充分利用系統中各個分量之間的相互作用,允許反應項的適度增長性,可容納相當廣泛的(特別是具實際背景的)反應擴散方程組,從而將解的存在性的證明大大簡化(見套用數學學報17 (1994),578--584; Proc. Roy. Soc. Edinburgh 130A (2000),1165-1180),得到多位國內外專家的肯定和好評.
⑷關於反應擴散方程組中臨界增長性的分析研究(國家自然科學基金項目“關於反應擴散方程組臨界增長性的分析及其數值模擬”,19871008).主要工作見 Math. Methods Appl. Sci. 22 (1999),43-54(SCI); J. Math. Anal. Appl. 232 (1999),293--311; Nonlinear Anal. 39 (2000),327--340.已引起國內外同行的注意,被多次引用. 得到著名數學家J. Serrin(美國科學院院士)的好評.
⑸關於非線性雙曲守恆律組廣義解的穩定性和唯一性的研究(見 J. Math. Res. Exposition 5 (1985),89--93; Acta Math. Sci. 4 (1984),443--454; Proc. Amer. Math. Soc. 96 (1986),295-296),改進和推廣了著名數學家R. DiPerna的重要工作,得到DiPerna本人的充分肯定.
為美國“數學評論”(Mathematical Reviews)撰寫這些領域的評論150餘則.

2000年前以本人為唯一作者的文章

以下為2000年前以本人為唯一作者的部分工作(限於列舉被SCI檢索的國外期刊文章).
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)

2002年後與學生合作發表的文章

以下為2002年後與學生合作發表的部分文章(僅限於列舉屬於SCI檢索的國外期刊文章.國家自然科學基金項目“多重非線性拋物方程組的臨界指標與解的奇性傳播”,10471013):
Sining Zheng,Lizhong Zhao and Feng 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)
Xianfa Song and Sining Zheng,Multi-nonlinear interactions in quasilinear reaction-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. Letters 19 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 information 10.1016/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 information 10.1016/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)

所受獎勵

政府特殊津貼
寶鋼教育基金優秀教師特等獎(2000)
大連理工大學首屆教學名師獎(2003)
遼寧省優秀教學成果一等獎(2002)
遼寧省優秀教學成果一等獎(2005)
遼寧省自然科學學術成果一等獎(2003)
遼寧省自然科學學術成果一等獎(2007)
遼寧省教學名師獎(2007)

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