Sets of unique continuation for heat equation

Nikolai Nadirashvili (1) , Nadezda Varkentina (2)

1 I2M - Institut de Mathématiques de Marseille
2 UB - Université Sciences et Technologies - Bordeaux 1

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. Our results are motivated by some applied problems. They related to classical problems of the unique continuation and the backward uniqueness for parabolic equations.

Mots clés: heat equation; nodal set; parabolic equations

Domaines: Equations aux dérivées partielles [math.AP]; Thermique [physics.class-ph]; Physique mathématique [math-ph]

Nikolai Nadirashvili, Nadezda Varkentina. Sets of unique continuation for heat equation. Potential Analysis, 2014, 41 (4), pp.1267--1272. ⟨10.1007/s11118-014-9419-4⟩. ⟨hal-01335895⟩