Nonlinear partial differential equations, including: scalar conservation laws, Euler equations, Stochastic differential equations, Hamilton-Jacobi equations, etc..

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September 2009–June 2014:   University of Chinese Academy of Sciences        Ph. D. (Mathematics)

                    Advisor: Professor Xiaozhou Yang

September 2005–June 2009:   Zhengzhou University (Henan Province)              B. S. (Mathematics)

Oct. 2017- Present: Associate Professor, Campus of Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, CAS, Wuhan 430071, China

​Jul. 2014-Sep. 2017: Assistant Professor, Wuhan Institute of Physics and Mathematics, CAS, Wuhan, China

Mar.2025–Apr. 2025: Academic Visitor, Academy of Mathematics and Systems Science, CAS, Beijing, China, Inviter: Feimin Huang

Jan. 2025–Jan. 2025: Academic Visitor, Academy of Mathematics and Systems Science, CAS, Beijing, China, Inviter: Feimin Huang

Sep. 2024–Jul. 2024: Academic Visitor, Academy of Mathematics and Systems Science, CAS, Beijing, China, Inviter: Feimin Huang

Jan. 2024–Feb. 2024: Visiting Scholar, City University of Hong Kong, Hong Kong, China, Inviter: Wei Xiang

Jul. 2022–Jul. 2023:   Visiting Scholar, University of Oxford, Oxfordshire, UK, Inviter: Gui-Qiang G. Chen

Oct. 2018–Nov. 2018: Visiting Scholar, City University of Hong Kong, Hong Kong, China, Inviter: Wei Xiang

Jun. 2017–Aug. 2017: Visiting Scholar, City University of Hong Kong, Hong Kong, China, Inviter: Wei Xiang

Oct. 2016–Nov. 2016: Visiting Scholar, City University of Hong Kong, Hong Kong, China, Inviter: Wei Xiang

Nov. 2015–Jan. 2016: Visiting Scholar, City University of Hong Kong, Hong Kong, China, Inviter: Wei Xiang

   

1.Gaowei Cao, Feimin Huang, and Guirong Tong, Formula for Entropy Solutions of the 1D Pressureless Euler–Poisson System: Well-Posedness of Entropy Solutions and the Asymptotic Behavior, Proc. Steklov Inst. Math. 330(1) (2025), 22–62.

2.Gaowei Cao and Gui-Qiang G. Chen, Minimal entropy conditions for scalar conservation laws with general convex fluxes, Quarterly of Applied Mathematics. 81(3) (2023), 567-598.

3. Gaowei Cao, Hui Kan, Wei Xiang, and Xiaozhou Yang, Smooth solution of multi-dimensional non-homogeneous conservation law: its formula, and necessary and sufficient blowup criterion, Acta Math. Appl. Sin., Engl. Ser. 39(1) (2023), 17–27.

4. Guiqin Qiu, Gaowei Cao, Xiaozhou Yang, and Yuan-An Zhao, Envelope methods and more general new global structures of solutions for multi-dimensional conservation law, Commun. Appl. Math. Comput. 5(3) (2023), 1180-1234.

5. Guiqin Qiu, Gaowei Cao, and Xiaozhou Yang, Structures of interaction of non-selfsimilar elementary waves for 2D scalar conservation law with two initial discontinuities, Acta Math. Appl. Sin., Engl. Ser. 39(3) (2023), 465-490 .

6. Yuan-An Zhao, Gaowei Cao, and Xiaozhou Yang, Global solutions and interactions of non-selfsimilar elementary waves for n-D non-homogeneous Burgers equation, Acta Math. Appl. Sin., Engl. Ser. 39(4) (2023), 830-853.

7.Gaowei Cao, Wei Xiang, and Xiaozhou Yang, Global structure of admissible solutions for multi-dimensional non-homogeneous scalar conservation law with Riemann-type data, J. Differential Equations. 263(2) (2017), 1055-1078.

8. Kai Hu, Gaowei Cao, and Xiaozhou Yang, Non-selfsimilar global solutions and their structure for the multi-dimensional combustion models, Acta Math. Appl. Sin., Engl. Ser. 33(3) (2017), 659-678.

9. Gaowei Cao, Kai Hu, and Xiaozhou Yang, Envelope and classification of global structures of solutions for a class of two-dimensional conservation laws, Acta Math. Appl. Sin., Engl. Ser. 32(3) (2016), 579-590.

10. Chunlong Yang, Gaowei Cao, and Xiaozhou Yang, Uniform formula for the Riemann solutions of a scalar combustion model, Acta Math. Sci., Engl. Ed. 36B(5) (2016), 1405-1418.

11. Gaowei Cao, Kai Hu, and Xiaozhou Yang, A formula of global smooth solution for non-homogeneous multi-dimensional conservation laws with unbounded initial value, Acta Math. Sci., Engl. Ed. 35B(2) (2015), 508-526.

12. Kai Hu, Gaowei Cao, and Xiaozhou Yang, Riemann problems for three-dimensional combustion models, Acta Math. Appl. Sin., Engl. Ser. 30(2) (2014), 321-346. 

Cao's main research areas lie in the mathematical analysis of nonlinear partial differential equations, especially nonlinear equations of hyperbolic conservation laws, the Hamilton-Jacobi equations, pressureless Euler/Euler-Poisson flows, stochastic partial differential equations, and combustion models. His recent research interests mainly focus on: Formula for entropy solutions, fine structures of entropy solutions and asymptotic behaviors of entropy solutions of hyperbolic conservation laws, pressureless Euler and Euler-Poisson flows, and stochastic partial differential equations; as well as invariant measures, entropy conditions, formula for smooth solutions, and non-selfsimilar structures of Riemann solutions.