This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physical and Life Sciences, held in Bad Herrenalb, Germany.
Table of Contents
Part 1 Semigroups and partial differential equations: different domains induce different heat semigroups on C0(omega); Gaussian estimates for second order elliptic divergence operators on Lipschitz and C4 domains; approximate solutions to the abstract Cauchy problem; smart structures and super stability; on the structure of the critical spectrum; an operator-valued transference principle and maximal regularity on vector-valued Lp-spaces; on anomalous asymptotics of heat kernels; on some classes of differential operators generating analytic semigroups; a characterization on the growth bound of a semigroup via Fourier multipliers; Laplace transform theory for logarithmic regions; exact boundary controllability of Maxwell's condition for exponential dichotomy of parabolic evolution equations; edge-degenerate boundary value problems on cones; a theorem on products of noncommuting sectorial operators; the spectral radius, hyperbolic operators and Lyapunov's theorem; a new approach to maximal Lp-regularity. Part 2 Nonlinear evolution equations: the instantaneous limits of a reaction-diffusion system; a semigroup approach to dispersive waves; regularity properties of solutions of fractional evolution equations; infinite horizon Riccati operators in nonreflexive spaces; a hyperbolic variant of Simon's convergence theorem; solution of a quasilinear parabolic-elliptic boundary value problem. Part 3 Physical and life sciences: singular cluster interactions in few-body problems; Feynman and Wiener path integrals; spectral characterization of mixing evolutions in classical statistical physics; on stochastic Schrodinger equation as a Dirac boundary-value problem, and an inductive stochastic limit; a maximum principle for fully nonlinear parabolic equations with time degeneracy; Dirac algebra and Foldy-Wouthuysen transform. Part 4 Stochastic evolution equation.
GÜNTER LUMER is a Professor in the Department of Mathematics at the University of Mons-Hainaut, Mons. Belgium, and a member/researcher of the Solvay Institute for Physics and Chemistry, Brussels, Belgium. He is also President of the Contact Group on Partial Differential Equations of the Belgian National Fund for Scientific Research. The coeditor of Erolution Equations, Control Theory, and Biomathematics (Marcel Dekker, Inc.) and author or coauthor of over JOO professional papers and monographs. he is a member of the American Mathematical Society, the Belgian Mathematical Society, and the French Mathematical Society. Dr. Lumer received the M.Sc. degree ( 1957) in electrical engineering from the University of Montevideo, Uruguay, and the Ph.D. degree ( 1959) in mathematics from the University of Chicago, Illinois. LUTZ WEIS is Professor of Mathematics at the University of Karlsruhe, Germany. The author or coauthor of numerous professional papers on asymptotics, semigroups, spectral theory, and other topics, Dr. Weis is a member of the American Mathematical Society and the German Mathematical Society. He received the Ph.D. degree (1974) in mathematics from the University of Bonn, Germany.