Evolution Semigroups in Dynamical Systems and Differential Equations

Abstract

70 Carmen Chicone and Yuri Latushkin, Evolution semigroups in dynamical systems and differential equations, 1999 69 C. T. C. Wall (A. A. Ranicki, Editor), Surgery on compact manifolds, Second Edition, 1999 68 David A. Cox and Sheldon Katz, Mirror symmetry and algebraic geometry, 1999 67 A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Second Edition, 1999 66 Yu. Ilyashenko and Weigu Li, Nonlocal bifurcations, 1999 65 Carl Faith, Rings and things and a fine array of twentieth century associative algebra, 1999 64 Rene A. Carmona and Boris Rozovskii, Editors, Stochastic partial differential equations: Six perspectives, 1999 63 Mark Hovey, Model categories, 1999 62 Vladimir I. Bogachev, Gaussian measures, 1998 61 W. Norrie Everitt and Lawrence Markus, Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators, 1999 60 Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace C*-algebras, 1998

Regularization and frequency-domain stability of well-posed systems

“…In particular, one obtains the well known and important equality s 0 (A) = ω 0 (A) for a C 0 -semigroup on a Hilbert space (which is a consequence of Gearhart's theorem, [5], [16]). …”

ON ${\bf (a,b)}$ -DICHOTOMY FOR EVOLUTIONARY PROCESSES ON A HALF-LINE

“…Most of the concepts, presented some decades ago, (see for instance [3,4,11], or more recently [2]) are of the uniform type. It is wellknown that the most general concept of uniform dichotomy is the so-called ordinary dichotomy, which goes back to the book due to J. L. Massera and J. J. Schäffer [11].…”

“…In last few years, several results about exponential stability and exponential dichotomy for the case of exponentially bounded and strongly continuous evolution families were obtained by N. van Minh [13,14], F. Räbiger [13], Y. Latushkin [2,6,7,8], M. Pinto [1,18], T. Randolph [7,8], R.Rau [22], R. Sacker [24], G. Sell [24] and R. Schnaubelt [8,13,25], W. Zhang [26]. All these results are given for the uniform case.…”

Nonuniform exponential stability for evolution families on the real line

“…An important contribution in the study of the asymptotic behaviour of the dynamical systems described by the evolution families is represented by [3], published in 1999 by C. Chicone and Y. Latushkin. Another important results in the study of the evolution equations were obtained by B.M.…”