Name：Kai Yan

Phone：027-87543231

Address: No. 1037, Luoyu Road, Hongshan Zone, Wuhan, China

Academic Degrees

PhD, 2014, School of Mathematics, Sun Yat-sen University, Guangzhou, China;

Bachelor, 2008, Department of Mathematics, Nanchang University, Nanchang, China.

Professional Experiences

Hong Kong Scholar (2019-2021); Department of Mathematics, City University of Hong Kong;

Associate Professor (2018-present); School of Mathematics and Statistics, Huazhong University of Science and Technology;

Assistant Professor (2015-2018); School of Mathematics and Statistics, Huazhong University of Science and Technology;

PhD Joint Training Program (2012-2013); Institute for Applied Mathematics, Leibniz Universität Hannover, Germany.

Research Interests

Nonlinear Partial Differential Equations;

Qualitative Analysis for Shallow Water Wave Models.

Projects

National Natural Science Foundation of China：11501226, Studies on the well-posedness, blow up and global existence of strong solutions to the Cauchy problem for multi-component Camassa-Holm systems, 2016/01—2018/12.

Selected Publications

[1] Kai Yan, Z. Qiao, and Z. Yin, "Qualitative analysis for a new integrable two-component Camassa-Holm system with peakon and weak kink solutions," Communications in Mathematical Physics, vol. 336, pp. 581-617, 2015.

[2] Kai Yan, Z. Qiao, and Y. Zhang, "Blow-up phenomena for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions," Journal of Differential Equations, vol. 259, pp. 6644-6671, 2015.

[3] Kai Yan and Z. Yin, "On the Cauchy problem for a two-component Degasperis-Procesi system," Journal of Differential Equations, vol. 252, pp. 2131-2159, 2012.

[4] Kai Yan and Z. Yin, "Analytic solutions of the Cauchy problem for two-component shallow water systems," Mathematische Zeitschrift, vol. 269, pp. 1113-1127, 2011.

[5] Kai Yan and Z. Yin, "Initial boundary value problems for the two-component shallow water systems," Revista Matemática Iberoamericana , vol. 29, pp. 911-938, 2013.

[6] Kai Yan and Z. Yin, "Well-posedness for a modified two-component Camassa-Holm system in critical spaces," Discrete and Continuous Dynamical Systems, vol. 33, pp. 1699-1712, 2013.

[7] Kai Yan and Z. Yin, "On the initial value problem for higher dimensional Camassa-Holm equations," Discrete and Continuous Dynamical Systems, vol. 35, pp. 1327-1358, 2015.

[8] Kai Yan, Z. Qiao, and Y. Zhang, "On a new two-component b-family peakon system with cubic nonlinearity," Discrete and Continuous Dynamical Systems, vol. 38, pp. 5415-5442, 2018.

[9] Kai Yan and Z. Yin, "Infinite propagation speed and asymptotic behavior for a two-component Degasperis-Procesi system," Monatshefte für Mathematik, vol. 181, pp. 217-234, 2016.

[10] C. Guan, Kai Yan(corresponding author), and X. Wei, "Lipschitz metric for the modified two-component Camassa-Holm system," Analysis and Applications, vol. 16, pp. 159-182, 2018.

Awards:

2018  Scholarship Award of Huazhong University of Science and Technology;

2017  Teachers Teaching Competition of Huazhong University of Science and Technology (First Prize);

2013-2014  Excellent Doctoral Dissertation Cultivate Program of Sun Yat-sen University;

2012  National Scholarship for Doctoral Candidates.

Courses Taught

Functional Analysis;

Mathematical Analysis (I, II, III);

Applied Partial Differential Equations;

Linear Algebra.