楊晗

1995年在四川師範大學獲理學碩士學位，1998年在復旦大學數學所獲理學博士學位，師從李大潛院士、周憶教授。2002年10月至2004年5月在四川大學數學博士后流動站從事在職博士后研究工作，合作導師徐道義教授。1998年7月起任教於西南交通大學， 2000年任副教授，2003年任教授。主要從事非線性發展偏微分方程解的適定性方面（整體解的存在性、解的破裂、解的漸近性態）的理論研究。在上述領域發表學術論文40多篇(其中SCI檢索論文20多篇)，累計指導研究生近20名，其中一人獲校優秀碩士論文。先後主持國家自然科學基金1項，主研國家傑出青年基金和國家自然科學基金3項，主持和主研其它項目10餘項。

(1)主持國家自然科學基金（10301026）非線性發展方程的低正則適定性9萬（2003--2006）

(2)第一主研國家傑出青年基金（10225102）非線性波動方程的整體解70萬（2002-2005）

(3)第一主研國家自然科學基金（71003082/G0302）基於多方交易行為分析的供應鏈金融集成風險管理研究18萬2011-2012）

(4)第一主研國家自然科學基金（61203156）基於實際結構特徵的耦合複雜系統網路上滲流理論及級聯失效行為25萬（2013-2015）

主要論文目錄

(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系統在低能量空間中的整體適定性，數學年刊，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 空間中MHD方程組強解的存在唯一性及衰減性質，數學學報， 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) 一類弱耗散Camassa-Holm 方程Cauchy問題在Besov 空間解的局部適定性，數學年刊, 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)

(1)四川省第六屆學術帶頭人後備人選

(2)四川省教學成果獎二等獎1項

(3)西南交通大學教學成果獎一等獎1項.

課程教學

(1)本科課程：數學分析、實變函數、泛函分析、常微分方程、高等數學、點集拓撲學

(2)研究生課程：線性偏微分方程、非線性發展方程、拓撲學、數學物理方法