Abstract：

The 1965 paper of James Glimm on hyperbolic conservation laws inaugurates the modern shock wave theory. This classical paper inspires many works, starting with the difficult Glimm-Lax paper. There is now a well-posedness theory for systems of hyperbolic conservation laws in 1-D. The unique features of this fascinating development should have broad appeal in nonlinear analysis and PDEs. There is also the obvious question of how to generalize the Glimm theory to multi-D. This lecture will explain some of the main features of the Glimm theory, reminisce about related happenings, and make suggestions on possible ways for generalization of the Glimm theory.