Evolution Equations and Their Applications in Physical and Life Sciences

Abstract

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.