The Morse-Smale property for a semi-linear parabolic equation
نویسندگان
چکیده
منابع مشابه
The Morse-Smale Complex
The main aim of this paper is to present the construction of the Morse– Smale complex of a compact smooth manifold M with boundary and to establish the connection to the topology of M . This approach to connecting the analysis of an appropriate function f : M → R — respectively the dynamical system associated to such a function and a Riemannian metric g — with the topology of the manifold was i...
متن کاملHierarchical Morse - Smale Complexes for Piecewise Linear 2-Manifolds
We present algorithms for constructing a hierarchy of increasingly coarse Morse-Smale complexes that decompose a piecewise linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse-Smale complexes by canceling pairs of crit...
متن کاملMorse-Smale Regression.
This paper introduces a novel partition-based regression approach that incorporates topological information. Partition-based regression typically introduce a quality-of-fit-driven decomposition of the domain. The emphasis in this work is on a topologically meaningful segmentation. Thus, the proposed regression approach is based on a segmentation induced by a discrete approximation of the Morse-...
متن کاملMorse-Smale Decompositions for Modeling Terrain Knowledge
In this paper, we describe, analyze and compare techniques for extracting spatial knowledge from a terrain model. Specifically, we investigate techniques for extracting a morphological representation from a terrain model based on an approximation of a Morse-Smale complex. A Morse-Smale complex defines a decomposition of a topographic surface into regions with vertices at the critical points and...
متن کاملA Linearized Finite Difference Scheme with Non-uniform Meshes for Semi-linear Parabolic Equation
Abstract: In the present paper, a linearized difference scheme with non-uniform meshes for semi-linear parabolic equation is proposed. The scheme is constructed according to the change rule of the solution by travelling wave solution theory for partial differential equation. The existence and uniqueness of the numerical solution are derived by linear systems theory, and the convergence and stab...
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: Journal of Differential Equations
سال: 1986
ISSN: 0022-0396
DOI: 10.1016/0022-0396(86)90093-8