Gradient flows for bounded linear evolution equations
نویسندگان
چکیده
We study linear evolution equations in separable Hilbert spaces defined by a bounded operator. answer the question which of these can be written as gradient flow, namely those for operator is real diagonalisable. The proof constructive, from we also derive geodesic lambda-convexity.
منابع مشابه
Evolution semi-linear hyperbolic equations in a bounded domain
In this article, our goal is to prove the existence and uniqueness of solution for 1D and 2D semi-linear hyperbolic equations in a bounded domain with a monotone nonlinear term. We use elliptic regularization and a finite difference scheme in time to build the approximate solutions for the semi-linear hyperbolic equations, and we utilize the regularization method together with the monotonicity ...
متن کاملGradient evolution for potential vorticity flows
Two-dimensional unsteady incompressible flows in which the potential vorticity (PV) plays a key role are examined in this study, through the development of the evolution equation for the PV gradient. For the case where the PV is conserved, precise statements concerning topologyconservation are presented. While establishing some intuitively well-known results (the numbers of eddies and saddles i...
متن کاملGradient Flows and Double Bracket Equations
A unified extension of the gradient flows and the double bracket equations of ChuDriessel and Brockett is obtained in the frame work of reductive Lie groups. We examine the gradient flows on the orbit in the Cartan subspace of a reductive Lie algebra, under the adjoint action. The results of Chu-Driessel and Brockett are corresponding to the reductive groups GL(n,R) and O(p, q).
متن کاملGradient schemes for linear and non-linear elasticity equations
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numeri...
متن کاملBounded Solutions of Almost Linear Volterra Equations
Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. AMS Subject Classifications: 45D05, 45J05.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Zeitschrift für Analysis und ihre Anwendungen
سال: 2022
ISSN: ['0232-2064', '1661-4534']
DOI: https://doi.org/10.4171/zaa/1706