Spontaneous change of type is a widely observed phenomenon in physics. In this volume, leading experts survey from a mathematical point of view topics such as phase transitions in crystals, cluster dynamics, viscoelastic flows, motion of interfaces in thermodynamics, shocks in transonic flows, and nonlinear diffusion with finite speed of propagation. Owing to new mathematical techniques, there is now a renewed interest in these difficult questions. The present volume supplies new results but may also serve as an excellent introduction to recent literature. It will be of interest to researchers and to graduate students in physics and mathematics.
The contributions deal with changing-type phenomena from both physical and mathematical points of view. Among the topics discussed are spontaneous phase transitions in crystals, clusterdynamics, and shock phenomena in transonic flows. The book provides a good survey of recent developments in this active field of research.
Dynamics and minimizing sequences.- Discontinuous solutions of bounded variations to problems of the calculus of variations and of quasi linear hyperbolic differential equations. Integrals of Serrin and Weierstrass..- Minimizing sequences for nonconvex functionals, phase transitions and singular perturbations.- Dynamics of cluster growth.- A geometric approach to the dynamics of u t = ?2 u ?? + f(u) for small ?.- On the isothermal motion of a phase interface.- The relaxed invariance principle and weakly dissipative infinite dimensional dynamical systems.- Mathematical problems associated with the elasticity of liquids.- Analysis of spurt phenomena for a non-newtonian fluid.- Boundary conditions for steady flows of viscoelastic fluids.- The use of vectorfield dynamics in formulating admissibility conditions for shocks in conservation laws that change type.- On the Cauchy problem for the Davey-Stewartson system.- Inverse scattering and factorization theory.- Recent results on the Cauchy problem and initial traces for degenerate parabolic equations.- A nonlinear eigenvalue problem involving free boundaries.- Two nonlinear diffusion equations with finite speed of propagation.