In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Mathematical aspects of supersonic flow past wings, S-X. Chen; the null condition and global existence of solutions to systems of wave equations with different speeds, R. Agemi, K. Yokoyama; scaling limits for large systems of interacting particles, K. Uchiyama; regularity of solutions of initial boundary value problems for symmetric hyperbolic systems with boundary characteristic of constant multiplicity, Y. Yamamoto; on the half-space problem for the discrete velocity model of the Boltzmann equation, S. Ukai; on a decay rate of solutions to the one-dimensional thermoplastic equations of a half line - linear part, Y. Shibata; bifurcation phenomena for the Duffing equation, a. Matsumura; some remarks on the compactness method, A.V. Kazhikhov; percolation on fractal lattices - asymptotic behaviour of the correlation length, M. Shinoda. (Part contents).