On attractors of m-Hessian evolutions
Nina Ivochkina, Nadezda Filimonenkova
TL;DR
This paper investigates the long-term behavior of solutions to m-Hessian evolution equations, providing conditions under which solutions converge to stationary functions as time progresses.
Contribution
It offers new sufficient and near-necessary conditions for the convergence of solutions to stationary states in m-Hessian evolution problems.
Findings
Derived conditions for solution convergence
Identified stationary functions as asymptotic limits
Enhanced understanding of m-Hessian evolution dynamics
Abstract
We study the asymptotic behavior of C^2-evolutions u = u(x,t) under a given action of the m-Hessian evolution operators and boundary conditions. We obtain sufficient (close to necessary) conditions for the convergence of solutions to the first intial-boundary value problem for the m-Hessian evolution equations to stationary functions as t tends to infinity.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Geometry and complex manifolds