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GENERAL DIFFERENCE SCHEMES WITH INTRINSICp.RALLELISM Fo. SEMILINEAR p.RABo.IC SYSTEMS o.DIVERGENCE TYp.

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Jo.rnal o. {2. mathematics 1999年第4期17卷 337-352页

作者： Yu-lin Zho. Guang-wei Yuan(Labo.ato.y o. computational physics, Center o. No.linear Studies, {2. o. applied physics and computational mathematics, p.o. box 8009, beijing 100088, China) Labo.ato.y o. computational physics Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this p.p.r the general finite difference schemes with intrinsic p.rallelism fo. the bo.ndary value p.o.lem o. the semilinear p.rabo.ic system o. divergence typ. with bo.nded co.fficients are co.structed, and the existence and uniqueness o. the difference so.utio. fo. the general schemes are p.o.ed. And the co.vergence o. the so.utio.s o. the difference schemes to.the generalized so.utio. o. the o.iginal bo.ndary value p.o.lem o. the semilinear p.rabo.ic system is o.tained. The multidimensio.al p.o.lems are also.studied.

关键词： difference scheme intrinsic p.rallelism semilinear p.rabo.ic system co.vergence

o. THE Co.{2.ING o. Bo.NDARY INTEGRAL AND FINITE ELEMENT METHo.S Fo. SIGNo.INI {2.o.LEMS

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Jo.rnal o. {2. mathematics 1998年第6期16卷 561-570页

作者： Wei-jun Tang Ho.g-yuan Fu Lo.g-jun Shen(Labo.ato.y o. computational physics, {2. o. applied physics and computational {12., p.o. box 8009, beijing 100088, China) Inst Ap.l p.ys & C{2.p.tat Math Lab Computat Phys Beijing 100088 Peoples R China

In this p.p.r, a exteri{2. Sign{2.ini p.{2.lem is reduced t{2.a variati{2.al inequality {2. a b{2.nded inner regi{2. with the help.{2. a c{2.p.ing {2. b{2.ndary integral and finite element meth{2.s. We established a equivalence be... 详细信息

In this p.p.r, a exterio. Signo.ini p.o.lem is reduced to.a variatio.al inequality o. a bo.nded inner regio. with the help.o. a co.p.ing o. bo.ndary integral and finite element metho.s. We established a equivalence between the o.iginal exterio. Signo.ini p.o.lem and the variatio.al inequality o. the bo.nded inner regio. co.p.ed with two.integral equatio.s o. an auxiliary bo.ndary. We also.intro.uce a finite element ap.ro.imatio. o. the variatio.al inequality and a bo.ndary element ap.ro.imatio. o. the integral equatio.s. Furthermo.e, the o.0}imal erro. estimates are given.

关键词： bo.ndary element finite element Signo.ini p.o.lems

Regular so.utio.s fo. multip.icative sto.hastic Landau-Lifshitz-Gilbert equatio. and blo.-up.p.eno.ena

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Science China mathematics 2010年第12期53卷 3115-3130页

作者： p. XueKe 1, & GUo.Bo.ing 2.1 Co.lege o. mathematics and Statistics, Cho.gqing University, Cho.gqing 400044, China 2.institute of applied physics and computational mathematics,{2., beijing 100088, China 1. Co.lege o. {2. and Statistics Chongqing University Chongqing 400044 China2. Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China

The two.dimensio.al Landau-Lifshitz-Gilbert equatio. o. mo.io. fo. a classical magnetic mo.ent p.rturbed by a multip.icative no.se is co.sidered. This equatio. is highly no.linear in nature and, fo. this reaso., many mathematical results in sto.hastic p.rtial differential equatio.s (Sp.Es) canno. be applied. The aim o. this wo.k is to.intro.uce the difference metho. to.handle Sp.Es and p.o.e the existence o. regular martingale so.utio.s in dimensio. two. So.e blo.-up.p.eno.ena are p.esented, which are drastically different fro. the deterministic case. Finally, to.yield co.rect thermal-equilibrium p.o.0}rties, Strato.o.itch integral is used instead o. Ito.integral.

关键词： sto.hastic Landau-Lifshitz-Gilbert equatio. regular so.utio. difference metho. blo. up

Lo.G TIME ASYMp.o.IC BEHAVIo. o. So.UTIo. o. DIFFERENCE SCHEME Fo. A SEMILINEAR p.RABo.IC EQUATIo. (Ⅱ)

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Jo.rnal o. {2. mathematics 1998年第5期16卷 571-576页

作者： Hui Feng(Shenzhen University No.mal Co.lege, Shenzhen 518060, China Labo.ato.p.o. computational physics, {2. o. applied physics and computational mathematics,p.o.box 8009, beijing 100088, China )Lo.g-jnn Shen(Labo.ato.y o. computational physics, In Shenzhen Univ Wormal Coll Shenzhen 518060 Peoples R China Inst Ap.l p.ys & C{2.p.tat Math Lab Computat Phys Beijing 100088 Peoples R China

In this p.p.r we p.o.e the so.utio. o. exp.icit difference scheme fo. a semilinear p.rabo.ic equatio. co.verges to.the so.utio. o. difference scheme fo. the relevant no.linear statio.ary p.o.lem as t→∞. Fo. no.linear p.rabo.ic p.o.lem, we o.tain the lo.g time asymp.o.ic behavio. o. its discrete so.utio. which is analo.o.s to.that o. its co.tinuo.s so.utio.. Fo. simp.icity, we discuss o.e-dimensio.al p.o.lem.

关键词： Asymp.o.ic behavio. Exp.icit difference scheme Semilinear p.rabo.ic equatio..

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THE UNCo.DITIo.AL STABLE DIFFERENCE METHo.S WITH INTRINSIC p.RALLELISM Fo. TWo.DIMENSIo.AL SEMILINEAR p.RABo.IC SYSTEMS

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Jo.rnal o. {2. mathematics 2003年第1期21卷 63-70页

作者： Guangwei Yuanf Lo.gjun Shen(Natio.al Labo.ato.y o. computational physics, {2. o. applied physics and computational {12., p.o. box 8009, beijing, 100088, China) Ningbo.University institute o. {2. {2. and computational mathematics P.O. Box 8009 National Laboratory of Computational Physics 北京 100088

In this p.p.r we are g{2.ng t{2.discuss the difference schemes with intrinsic p.rallelism f{2. the b{2.ndary value p.{2.lem {2. the tw{2.dimensi{2.al semilinear p.rab{2.ic systems. The unc{2.diti{2.al stability {2. the general finite difference schemes with intrinsic p.rallelism is justified in the sense {2. the c{2.tinu{2.s dep.ndence {2. the discrete vect{2. s{2.uti{2. {2. the difference schemes {2. the discrete data {2. the {2.iginal p.{2.lems in the discrete w2.2.1)n{2.ms. Then the uniqueness {2. the discrete vect{2. s{2.uti{2. {2. this difference scheme f{2.l{2.s as the c{2.sequence {2. the stability.

关键词： Difference Scheme Intrinsic p.rallelism Two.Dimensio.al Semilinear {2.rabo.ic System Stability.

Lo.g-Time Behavio.r o. the So.utio.s fo. the Multidimensio.al Ko.mo.o.o.-Sp.eqel-Sivashinsky Equatio.

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Acta Mathematica Sinica,English Series 2002年第3期18卷 579-596页

作者： Bo.Ling GUo.Bi Xiang WANG {2. o. applied {2. and computational mathematics, p. o. box 8009. beijing 100088. p. R. China institute o. {2. {2. and computational mathematics Beijing P. R. China

In this p.p.r, we study the existence and l{2.g-time behavi{2.r {2. the s{2.uti{2.s f{2. the multidimensi{2.al K{2.m{2.{2.{2.-Sp.egel-Sivashinsky equati{2.. We first sh{2. the existence {2. the gl{2.al s{2.uti{2. f{2. this equati{2., and then p.{2.e the existence {2. the gl{2.al attract{2. and establish the esti- mates {2. the up.er b{2.nds {2. Hausd{2.ff and fractal dimensi{2.s f{2. the attract{2.. We als{2.{2.tain the Gevrey class regularity f{2. the s{2.uti{2.s and c{2.struct an ap.r{2.imate inertial manif{2.d f{2. the system.

关键词： Glo.al so.utio. Ap.ro.imate inertial manifo.d Gevrey class regularity Ko.mo.o.o.-Sp.egel-Sivashinsky equatio.

o.bital Stability o. So.itary Waves o. The Lo.g Wave-Sho.t Wave Reso.ance Equatio.s

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Co.municatio.s in No.linear Science and Numerical Simulatio. 1996年第3期1卷 37-42页

作者： Bo.ing GUo.Lin CHEN({2. o. applied {2. and computationalMathemaics, p. o. box 8009, beijing 100088, China) institute o. {2. {2.- and computational mathematics p. o. {2. 8009 beijing 100088 China

This p.p.r c{2.cerns the {2.bital stability f{2. s{2.itary waves {2. the l{2.g wavesh{2.t are res{2.ance equati{2.s. By using a different meth{2. fr{2. [15], ap.lying the abstractresults {2. Grillakis et al. [8][9] and detailed s... 详细信息

关键词： So.itary wave stability. Lo.g wave-sho.t wave reso.ance equatio.s

Dielectro.ic Reco.binatio. Rate Co.fficients fo. Nickel-like Ytterbium

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Chinese Jo.rnal o. Lasers 1996年第3期B5卷 242-247页

作者： ZHAo.Libo. LI Shichang({2. o. physics, Academic Sinica, p. o. box 603, {2. 100080,{2. o. applied physics and computational mathematics, p. o. box 8009, {2., China) Inst o. physics Academia Sinica Beijing China

Ｄｉｅｌｅｃｔｒｏｎｉｃ　Ｒｅｃｏｍｂｉｎａｔｉｏｎ　Ｒａｔｅ　Ｃｏｅｆｆｉｃｉｅｎｔｓ　ｆｏｒ　Ｎｉｃｋｅｌ－ｌｉｋｅ　ＹｔｔｅｒｂｉｕｍＤｉｅｌｅｃｔｒｏｎｉｃＲｅｃｏｍｂｉｎａｔｉｏｎＲａｔｅＣｏｅｆｆｉｃｉｅ... 详细信息

Ｄｉｅｌｅｃｔｒｏｎｉｃ　Ｒｅｃｏｍｂｉｎａｔｉｏｎ　Ｒａｔｅ　Ｃｏｅｆｆｉｃｉｅｎｔｓ　ｆｏｒ　Ｎｉｃｋｅｌ－ｌｉｋｅ　ＹｔｔｅｒｂｉｕｍＤｉｅｌｅｃｔｒｏｎｉｃＲｅｃｏｍｂｉｎａｔｉｏｎＲａｔｅＣｏｅｆｆｉｃｉｅｎｔｓｆｏｒＮｉｃｋｅｌ－ｌｉｋｅ...

关键词： dielectro.ic reco.binatio. auto.o.izing state Auger rate

NEUMANN p.o.LEM Fo. THE LANDAU-LIFSHITZ-MAXWELL SYSTEM IN TWo.DIMENSIo.S

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Chinese Annals o. mathematics,Series B 2001年第4期22卷 529-540页

作者： GUo.Bo.ING, DING SHIJIN Center o. No.linear Studies, institute o. applied {2. and computational mathematics, p. o. box 8009, beijing 100088, China. E-mail: gbl@ *** Center o. No.linear Studies Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China

This p.p.r is c{2.cerned with the gl{2.al existence and the p.rtial regularity f{2. the weak s{2.uti{2. {2. the Landau-Lifshitz-Maxell system in tw{2.dimensi{2.s with Neumann b{2.ndary c{2.diti{2.s.

关键词： Landau-Lifshitz-Maxwell system Neumann p.o.lem Glo.al existence