杨晗

时间:2023-12-13 19:56:12编辑:莆田seo君
人物经历早年经历

1995年在四川师范大学获理学硕士学位,1998年在复旦大学数学所获理学博士学位,师从李大潜院士、周忆教授。2002年10月至2004年5月在四川大学数学博士后流动站从事在职博士后研究工作,合作导师徐道义教授。1998年7月起任教于西南交通大学, 2000年任副教授,2003年任教授。主要从事非线性发展偏微分方程解的适定性方面(整体解的存在性、解的破裂、解的渐近性态)的理论研究。在上述领域发表学术论文40多篇(其中SCI检索论文20多篇),累计指导研究生近20名,其中一人获校优秀硕士论文。先后主持国家自然科学基金1项,主研国家杰出青年基金和国家自然科学基金3项,主持和主研其它项目10余项。

科学研究

(1)主持国家自然科学基金(10301026)非线性发展方程的低正则适定性9万(2003--2006)

(2)第一主研国家杰出青年基金(10225102)非线性波动方程的整体解70万(2002-2005)

(3)第一主研国家自然科学基金(71003082/G0302)基于多方交易行为分析的供应链金融集成风险管理研究18万2011-2012)

(4)第一主研国家自然科学基金(61203156)基于实际结构特征的耦合复杂系统网络上渗流理论及级联失效行为25万(2013-2015)

主要论文目录

(1) Scattering for semilinear wave equations with small data in high space dimensions, J. Partial Differential Equations, 12 (1999), No: 1, 26—40

(2) A singular perturbation problem for semilinear wave equations with small parameter, Discrete Contin. Dynam. Systems, 5 (1999), No: 3, 473--488.

(3) On the diffusion phenomenon for quasilinear hyperbolic waves I, l Chinese Ann. Math. Ser. B, 21 (2000), No: 1, 63--70. (with A. J. Milani).

(4) On the diffusion phenomenon for quasilinear hyperbolic waves II, Bull. Sci. Math., 124 (2000), No: 5, 415--433. (with A. J. Milani).

(5) $L^1$ estimates for dissipative wave equations, Math. Methods in Appl. Sci., 24 (2001), No: 5, 319--338. (with A. J. Milani).

(6) Remarks on the lifespan for the solution to nonlinear wave equations in three space dimensions, Acta Mathematica Scientia, 23 (2003), No: 1, 16-22.(with F.~Liu).

(7) On the Cauchy problem for Klein-Gordon Schr"odinger systems with rough data, Discrete and Continuous Dynamical Systems, Vol 12, No.2, 2005, 233-242

(8) The self-similar solutions to some nonlinear integro-differential equation corresponding to fractional order time derivative, Acta Mathematica Sinica, English Serires, Published online: Sept, 5, 2005.(with C.~Miao).

(9) Global existence for semilinear wave equations in exterior domain, Acta Mathematica Scientia (in Chinese), 2007. (with H. Wu)

(10) Davey—Stewartson系统在低能量空间中的整体适定性,数学年刊,2009。(with N. Yang)

(11) Global well-posedness results for Davey-Stewartson systems below the nergy norm, Chinese Journal of Contemporary Mathematics, 2009. (with N. Yang)

(12) Expontential attractor and its fractal dimension for a second order lattice dynamical system, Journal of Mathematical Analysis and Applications, 2009.(with X. M. Fan)

(13) Existence and uniqueness for strong solutions of the generlaized MHD eqautions, Nonlinear Functional Analysis and Applications, Vol. 14, 3(2009), 439-452. (with X. K. Luo)

(14) Limiting profile of the blow-up solutions of the fourth-order nonlinear Schrodinger equation, Dyn. Partial Differ. Equ, 2010 (with Shihui Zhu, Jian Zhang)

(15) L pc-concentration of blow-up solutions for the biharmonic nonlinear Schr?dinger equation, Applicable Analysis, 2010 (with Shihui Zhu, Jian Zhang).

(16) Biharmonic nonlinear Schrodinger equation and the profile decomposition, Nonlinear Analysis, 2011. (with Shihui Zhu, Jian Zhang).

(17) Blow-up of the rough solution to the fourth-order nonlinear Schrodiner equation, Nonlinear Analysis, 2011. (with Shihui Zhu, Jian Zhang)

(18) PL^n∩PL^p 空间中MHD方程组强解的存在唯一性及衰减性质,数学学报, Vol. 54, 1(21011), 31-40. (with X. K. Luo)

(19) Global existence of solutions for damped wave equations with nonlinear memory,Applicable Analysis, 2012.

(20) Global Analysis for Rough Solutions to the Davey-Stewartson System,Abstract and Applied Analysis,2013.

(21) 一类弱耗散Camassa-Holm 方程Cauchy问题在Besov 空间解的局部适定性,数学年刊, 2013.

(22) Global Conservative Solutions of a Generalized Two-Component Camassa-Holm System,Journal of Applied Mathematics,Volume 2014, Article ID 613851, 12 pages. (with Feng. Zhang, Yonghong Wu).

(23) The Cauchy Problem for a Weakly Dissipative 2-Component Camassa-Holm System, Mathematical Problems in Engineering,Volume 2014 , Article ID 801941, 16 pages.(with Sen Ming, Yonghong Wu).

(24) Blow-up criteria for the inhomogeneous nonlinear Schr?dinger equation, Journal of Inequalities and Applications, 2014:55, 8 pages. (with Shihui Zhu).

(25) Asymptotic behaviors of solutions to the dissipative 2-component Degasperis-Procesi dissipative 2-component Degasperis-Procesi system,Boundary Value Problems,2014(with Sen Ming) .

(26) Blow-up Rate, Mass Concentration and Asymptotic Profile of Blow-up Solutions for the Nonlinear Inhomogeneous Schrodinger Equation, Accepted by Applied Mathematics and Computation, 2014(with Shihui Zhu)

主要成就

(1)四川省第六届学术带头人后备人选

(2)四川省教学成果奖二等奖1项

(3)西南交通大学教学成果奖一等奖1项.

课程教学

(1)本科课程:数学分析、实变函数、泛函分析、常微分方程、高等数学、点集拓扑学

(2)研究生课程:线性偏微分方程、非线性发展方程、拓扑学、数学物理方法

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