Abstract
AbstractGeneralized $$\Lambda$$
Λ
-semiflows are an abstraction of semiflows with nonperiodic solutions, for which there may be more than one solution corresponding to given initial data. A select class of solutions to generalized $$\Lambda$$
Λ
-semiflows is introduced. It is proved that such minimal solutions are unique corresponding to given ranges and generate all other solutions by time reparametrization. Special qualities of minimal solutions are shown. The concept of minimal solutions is applied to gradient flows in metric spaces and generalized semiflows. Generalized semiflows have been introduced by Ball.
Funder
Technische Universität München
Publisher
Springer Science and Business Media LLC
Reference26 articles.
1. Ambrosio, L., Fusco, N., Pallara, D.: Functions of bounded variation and free discontinuity problems. In: Oxford Mathematical Monographs. Clarendon Press, Oxford (2000)
2. Ambrosio, L., Gigli, N., Savaré, G.: Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in mathematics ETH Zürich, Birkhäuser, Basel (2005)
3. Babin, A.V.: Attractor of the generalized semigroup generated by an elliptic equation in a cylindrical domain. Izv. Math. 44, 207–223 (1995)
4. Babin, A.V., Vishik, M.I.: Maximal attractors of semigroups corresponding to evolution differential equations. Sb. Math. 54, 387–408 (1986)
5. Ball, J.: Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations. In: Mechanics: From Theory to Computation, pp. 447–474. Springer, Cham (2000)