An inverse source problem for the heat equation and the enclosure method

Abstract

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given.

23pages

References in corpus (3)

• Reconstruction of a source domain from the Cauchy data
• On reconstruction in the inverse conductivity problem with one measurement
• The Herglotz wave function, the Vekua transform and the enclosure method

Cited by in corpus (6)

• The enclosure method for the heat equation
• The framework of the enclosure method with dynamical data and its applications
• Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
• Two analytical formulae of the temperature inside a body by using partial lateral and initial data
• Extracting discontinuity using the probe and enclosure methods
• Reconstruction of a source domain from the Cauchy data: II. Three dimensional case