报告题目：Hyperbolic conservation laws in one space dimension: old and new

报告人：Alberto Bressan, Eberly Family Chair Professor of Mathematics, Penn State University

报告时间：2024年7月10日（周三）9:30

报告地点：20-404

报告摘要：Hyperbolic conservation laws provide the basic mathematical models for continuum physics.  A typical example is provided by the Euler equations of gas dynamics, accounting for the conservation of mass,  momentum and energy.

The first part of the talk will review the basic concepts in the theory of hyperbolic conservation laws, including: weak solutions  admissibility conditions, existence and continuous dependence of solutions to the initial value problem.

The second part will cover some very recent advances concerning the uniqueness of entropy admissible solutions. Implications of these results toward a posteriori error estimates  for numerical approximations will be discussed, together with some open questions.

报告人简介：Alberto Bressan，美国宾州州立大学Eberly Family讲席教授，主要从事双曲守恒律、非线性波动方程、控制理论、非合作微分策略等问题的研究。2002年国际数学家大会一小时邀请报告人，美国数学会会士，曾获得G. Fichera prize, L. Amerio prize, Bôcher Memorial Prize, A. Feltrinelli prize, Analysis of Partial Differential Equations Prize of the SIAM等多项荣誉。担任十几个国际重要期刊的编委，包括Arch. Rational Mech. Anal., J. Differential Equations., SIAM J. Math. Anal., Discrete Contin. Dyn. Syst. 等。多次在国际会议上作邀请报告，发表超过200篇学术论文，在牛津大学出版社等出版多本专著。