Research

Team Leader:

XU Runzhang, a Professor and doctoral supervisor, third-level professor of Harbin Engineering University, young scholar of “Longjiang Scholar”. He is executive director of Heilongjiang Provincial Mathematical Society, young academic backbone of Heilongjiang Province, member of American Mathematical Society (AMS), commentator of American Mathematical Review (MR), member of International Mathematical Physics Union; Editor of Journal of Harbin Engineering University, Chief editor ofAdvances in Nonlinear Analysisin JCR1, Chief editor of Communications in Analysis and Mechanicsin SCI, Associate editor of Boundary Value Problems, SCI JCR1 journal, Editor ofApplied Numerical Mathematics, SCI JCR1 journal, SCI Search JCR1 journalElectronic Research Archive, ESCI search journalOpuscula Mathematica, Editorial board member ofThe Annals of the University of Craiova-Mathematics and Computer Science Series. He is the editorial board member of theBulletin of the Chinese Society of Industrial and Applied Mathematics, editorial board member of theJournal of Harbin Engineering University, Member of the Organizing Committee of the 14th, 16th, 18th, 19th and 21st Summer Workshops on Nonlinear Partial Differential Equations, member of the Academic Committee of the International academic conference IMACS. Professor Xu Runzhang has published 106 SCI papers inArchive for Rational Mechanics and Analysis,SIAM Journal on Mathematical Analysis,Journal of Functional Analysis,Journal of Differential Equations,Science China-Mathematicsand other high-level journals, including 56 in JCR District 1. and 22 papers in District 2, with a total citation frequency of 1682, and 7 papers with high ESI citation.

Team members:

YU Tao, Professor, a second-level professor of Harbin Engineering University, and a provincial famous teacher and a “lifelong demonstration lecturer” of HEU. His research field is applied mathematics. He has published a monograph, edited a national planning textbook, edited and participated in editing 7 teaching materials and auxiliary books. He has published more than 20 papers in journals like NA and APNUM.

GE Bin, an Associate Professor, and his research interest is nonlinear functional analysis and its application in partial differential equations, including variational and topological methods, partial differential equations, nonlinear analysis, multisolution research of variable exponential partial differential equations, multisolution and regularity of bidirectional dual partial differential equations. He has published more than 70 SCI papers in journals like ZAMP and JMP.

ZHANG Xuxi, an Associate Professor, and commentator of American Mathematical Review (MR), director of Heilongjiang Provincial Mathematical Society, director of Heilongjiang Provincial Industrial and Applied Mathematics Society, etc. His research interests include differential equation stability theory, nonlinear system control theory, adaptive control theory, coordinated control and interference suppression of multi-agent systems. He has published more than 30 papers in international journals such as IEEE Trans.Cir.& Sys., JFI and CNSNS.

SHANG Shaoqiang, an Associate Professor, his research interests include generalized inverse theory of set-valued metric Banach Spaces, geometric theory of special Banach Spaces Orlicz-Bochner Spaces, sphere covering theory of Banach Spaces, convex differential analysis of infinite dimensional Spaces. He has published more than 30 SCI papers in JFA and IJM journals.

WANG Ligang, an Associate Professor, is a member of the Youth Committee of the Northeast Center of Tianyuan Mathematics, and a member of the Educational Mathematics Committee of the Chinese Higher Education Association. His research direction is nonlinear dynamics of rotating machinery and stochastic numerical calculation. He has published 16 academic papers, including 8 SCI retrieval papers.

YANGYanbing, an Associate Professor, specializes in the theory of the well-fitting of nonlinear partial differential equations, focusing on the well-fitting problems of partial differential equations such as wave equation, parabola equation and Boussinesq equation, and the motion forms of water wave equations with rotation in the field of shallow water waves. He has published more than 30 SCI papers in DCDS and ZAMP journals.

LI Yanan, an Associate Professor, his research interests are the well-fitting theory of nonlinear wave equations and the solution of long-time dynamics. Focusing on the global stability of solutions of fractal-order dissipative Kirchhoff wave equation, Balakrishinan-Talor beam equation, quasi-linear wave equation satisfying non-standard growth conditions, viscoelastic model with time-dependent memory term, and the existence and stability of attractors. She has published 15 SCI papers in JDE and DCDS journals.

ZUO Bijun, a lecturer, her research direction is partial differential equations in fluid mechanics, focusing on the global existence of weak solutions to fluid mechanics equations, energy conservation problems of weak solutions to fluid mechanics equations and the existence and stability of steady vortex solutions. She has published 6 SCI papers in SIMA and JDE journals.

WANG Xingchang, a lecturer, his research interests include the stability of nonlinear development equations and water wave equations. He has published 10 SCI papers in JMP journals.

Teachers of the team cultivate 19 doctoral students, including 9 graduate doctoralstudents; cultivate 68 students with master’s degree, including 60 graduate students, , and guide 35 undergraduate graduation projects.

Main research direction:

1. Adaptive theory of nonlinear dynamical systems

In the past 20 years, the team has been committed to using potential well theory to study the dependence of the solution of nonlinear partial differential equation on the initial value, and for the three basic model equations of partial differential equation (wave equation, heat equation and Schrodinger equation). The study of fragmentation has been promoted to a systematic study under the same framework. It creates a new paradigm for the systematic study of the proper relationship between initial values and solutions.

2. fluid mechanics

Fluid mechanics is a discipline that studies the law of fluid movement, and it has important applications in aviation, aerospace, machinery, power, chemical industry, energy, environment and other professional fields. The core research object of fluid mechanics is nonlinear partial differential equations whose basic physical quantities of fluid such as density, velocity field, pressure and temperature are unknown functions. On the research of such issues, the research team has carried out in-depth cooperation with domestic and foreign research groups, including the University of Pittsburgh and the University of Texas.

3. Infinite dimensional dynamic system

For dissipative partial differential equations derived from many fields such as mechanics and physics. In most cases, the long-term dynamic behavior of their solutions can be studied by using the theory of infinite-dimensional dynamical systems. The existence, stability and geometric and topological structure of the attractors of infinite dimensional dynamical systems generated by dissipative partial differential equations are usually used to describe the long-term dynamic behavior of solutions. For research on such issues, our research team has carried out in-depth cooperation with domestic and foreign research groups, including Politecnico di Milano in Italy and Universidade de Sao Paulo in Brazil.

4. Thermal energy and combustible ice

Based on the discipline characteristics ofHarbin Engineering University, the research group has in-depth cooperation with the research group of the College of Power and Energy Engineering of our HEU, involving the research on combustible ice mining mechanism and technical research, two-phase flow model building and numerical simulation, droplet combustion technology and numerical simulation, phase balance calculation of various hydrates, flash technology and engineering applications, etc. Team leader Professor XU Runzhang has visited Princeton University, the University of Leeds, the University of Birmingham to carry out relevant interdisciplinary cooperation research, and as the only member of the mathematics discipline of China’s “Combustible Ice Advisory Committee”.

Teaching, Research projects and Awards

Academic works published by the team

Contact us:

Interested students are welcome to join the research team!We alsowelcomethedoctors, visiting scholars to join!

The team enrolls 1-2 post-doctors, 3-4 doctoral students, and 6-10graduatesevery year.

If undergraduatesare willingto join the teamtostudy in advance, please contact Ms. YANGYanbing (Email: yangyanbing@hrbeu.edu.cn).

WANG Xingchangwangxingchang@hrbeu.edu.cn

All students with a passion for mathematics are welcome to join us and discover what the world described by differential equations looks like!