This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga's 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell's equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga's extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.

Partial differential equations and mathematical fluid mechanics, Matthis Hieber (TU Darmstadt).- Applied mathematics and mathematical biology, Ryo Kobayashi (Hiroshima University).- Nonlinear partial differential equations, calculus of variations, phase transformations, and composite materials, Robert V. Kohn (Courant Institute, NYU).- Nonlinear partial differential equations, calculus of variations, and computations for complex fluids, Chun Liu (Penn State University).- Partial differential equations and mathematical fluid mechanics, Yasunori Maekawa (Tohoku University).- Mathematics and computations in meterology, and fluid mechanics, Alex Mahalov (Arizona State University).- Nonlinear partial differential equations, mathematics and computations for crystal growth, Takeshi Ohtsuka (Gunma University).- Calculus of variations and mathematical analysis of phase transitions, Piotr Rybka (University of Warsaw).- Partial differential equations and mathematical fluid mechanics, Jurgen Saal(Dusseldorf University).- Multi-scale modeling and computations, and computational interface problems, Richard Tsai (University of Texas).- Plasma physics and fluid mechanics, Zensho Yoshida (University of Tokyo).