Prof. Zhiqiang Shao
Fuzhou University, China
Title: The limits of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow with a source term
Abstract:
In this talk, we discuss the limits of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow with a Coulomb-like friction as the adiabatic exponent tends to one. Different from the homogeneous equations, the Riemann solutions of the inhomogeneous system are non self-similar. It is rigorously shown that, as the adiabatic exponent tends to one, any two-shock Riemann solution tends to a delta shock solution of the pressureless Euler system with a Coulomb-like friction, and the intermediate density between the two shocks tends to a weighted δ-mesaure which forms the delta shock; while any two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution of the pressureless Euler system with a Coulomb-like friction, whose intermediate state between the two contact discontinuities is a vacuum state. Moreover, we also give some numerical results to confirm the theoretical analysis. This is a joint work with Shouqiong Sheng.
Biography:
Zhiqiang Shao was born in Lanxi, Zhejiang, China in 1963. He got his undergraduate degree in Mathematics at Zhejiang Normal University, China in 1981. He also got his M.S. degree from Institute of Mathematics, Fudan University, China in 1991. He is now a Full Professor of applied mathematics at Fuzhou University, Fuzhou, China. He is also member in the Editorial Boards of several international journals： Modeling and Simulation (ISSN Print: 2324-8696; ISSN Online: 2324-870X)， Advances in Applied Mathematics (ISSN Print: 2324-7991; ISSN Online: 2324-8009), Theoretical Mathematics and Applications (ISSN: 1792-9687 (Print version); 1792-9709 (Online version) ),International Scientific Press, UK, JP Journal of Mathematical Sciences (ISSN:2248-7851), Ishaan Publishing House, INDIA， Journal of Applied & Computational Mathematics, ISSN: 2168-9679.
His research field includes nonlinear Partial Differential Equations and its applications, especially on applied partial differential equations and applications to Fluid Dynamics. He has published more than 40 papers indexed by SCI in famous academic journals such as Journal of Differential Equations, Nonlinear Analysis: Real World Applications, Nonlinear Analysis：Theory, Methods & Applications, Z. Angew. Math. Phys., Math. Models Methods Appl. Sci., Mathematical Methods in the Applied Sciences, J. Math. Anal. Appl., IMA J. Appl. Math., Communications on Pure and Applied Analysis, Journal of Elasticity, Math. Nachr., Acta Mathematica Scientia, Journal of Applied Analysis and Computation. He has visited Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, Institute for Mathematical Sciences, National University of Singapore, Singapore, University of Padova, Italy, the Chinese University of Hong Kong and Hong Kong Baptist University, and gave several forty-five (45) minute invited talks in international conferences and workshops, for example, the Fifth World Congress of Nonlinear Analysts (WCNA-2008).