Sets of unique continuation for heat equation

2014/03/06 by Nikolai Nadirashvili, Nikolaï Nadirashvili, Nadirashvili, Nikolai +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1403.1522

arxiv created 2014/07/01 · arxiv updated 2014/07/03

Abstract

We study nodal lines of solutions to the heat equations. We are interested in the global geometry of nodal sets, in the whole domain of definition of the solution. The local structure of nodal sets is a well understander subject, while the global geometry of nodal lines is much less clear. We give a detailed analysis of a simple component of a nodal set of a solution of the heat equation.

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