edited by S Kawashima (Kyushu University, Japan) & T Yanagisawa (Nara Women's University, Japan)

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)
• Blow-up, Life Span and Large Time Behavior of Solutions to a Weakly Coupled System of Reaction–Diffusion Equations (K Mochizuki)
• On a Decay Rate of Solutions to the One-Dimensional Thermoelastic Equations on 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 Behavior of the Correlation Length (M Shinoda)
• and other papers