Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics: EVEQ2000 Conference in Levico Terme (Trento, Italy), October 30–November 4, 2000(55 Progress in Nonlinear Differential Equations and Their Applications)

The seventh International Conference on Evolution Equations and their main areas of Applications (where the emphasis evolves as time and problems change) was held October 30 to November 4 at the CIRM (Centro Internazionale per la Ricerca Matematica) in Trento, Italy. In keeping with the basic principles and the recent tendencies governing these International Conferences, it brought together many of the world's leading experts in the fields mentioned, with particular effort on facilitating the interaction of established scientists and emerging young promising researchers, as well as the interaction of pure and applied specialists. In the latter directions, emphasis was extended here to include in addition to Physical and Life Sciences, also Industry and Economics. Topics among the recent advances treated here concern new developments in: moving boundary problems, asymptotics in non-linear Volterra equations and other asymptotics related developments, Poincare inequality on stratified sets, time operator and Markov processes in physics related advances, behavior of granu­ lar matter, stochastic aspects of Hamilton-Jacobi-Bellman equation, very general Paley-Wiener results applied to both classical and generalized functions, Ornstein­ Uhlenbeck operators and processes, quasilinear PDEs with memory operators, semi-group approach in economics (pricing theory) and other semi-group related developments, convolution-evolution equation in aeroelasticity, new developments in the study of age-structured models, new developments in maximal regularity.

Table of Contents:
Preface.- Evolution problems associated to linear growth functionals: the Dirichlet problem.- Time operators associated to dilations of Markov processes.- Boundary-value problems for systems of Hamilton-Jacobi-Bellman inclusions with constraints.- On a convolution-evolution equation in aeroelasticity.- On the effect of small delays to the stability of feedback systems.- Mean square continuity of Ornstein-Uhlenbeck processes in Banach spaces.- Some remarks on maximal regularity of parabolic problems.- A semigroup approach to no-arbitrage pricing theory: constant elasticity variance model and term structure models.- Perturbations of Ornstein-Uhlenbeck operators: an analytic approach.- Towards an L1-theory for vector-valued elliptic boundary value problems.- On moving boundaries in elliptic-parabolic systems.- Spectral mapping theorems and spectral space-independence.- The Laplacian with generalized Wentzell boundary conditions.- Consistency and stabilization of rational approximation schemes for Co-semigroups.- Poincaré’s inequality on stratified sets and applications.- Variational principles for granular matter.- Homogeneous dynamical systems and the age-structured SIR model with proportionate mixing incidence.- Asymptotic behaviour of solutions of nonlinear Volterra equations.- Semigroups for initial boundary value problems.- Maximal Lp-regularity for second order elliptic operators with uniformly continuous coefficients on domains.- An age structured S.I. epidemic problem in a heterogeneous environment.- A general “isotropic” Paley-Wiener theorem and some of its applications.- Asymptotic stability for a functional differential equation in Hilbert space.- Self-intersections for Willmore flow.- Chernoff's theorem and the construction of semigroups.- Harmonic mapheat flow generated by Markovian semigroups.- The Hamilton-Jacobi-Bellman equation and the stochastic Noether theorem.- Marcinkiewicz and Mihlin multiplier theorems, and R-boundedness.- Quasilinear P.D.E.s with memory operators.