Minimizing movements for dissipative systems that are not gradient flows
Volume 70 / 2022
Bulletin Polish Acad. Sci. Math. 70 (2022), 133-149
MSC: Primary 35K90; Secondary 35J20, 35K57.
DOI: 10.4064/ba221129-18-4
Published online: 10 May 2023
Abstract
The time discretization method, which is a method of constructing time global solutions for gradient flows, is applied to dissipative systems in Hilbert spaces, which are not necessarily gradient flows. Equations with perturbation terms added to gradient flows are considered, and when the perturbation term is smaller than the principal term in an analytical sense, the dissipative structure of the energy is maintained, and the existence of time global solutions is shown by the time discretization method.
