IDENTIFICATION AND CHARACTERIZATION OF A MOBILE SOURCE IN A GENERAL PARABOLIC DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS

We discuss an inverse source problem for a general parabolic differential equation in R-n x R+ with constant coefficients and a source whose strength and support may vary with time. We demonstrate that a knowledge of the solution on any bounded open set M in R-n located away from the source for any fixed time T >= 0 determines the so-called carrier support (originally defined in the article "Notions of support for far fields" [J. Sylvester, Inverse Problems, 22 (2006), pp. 1273-1288] as a nontrivial subset of the support of the true source) at that coincident time. Additionally, we provide a reconstruction algorithm which can locate the time-varying position of the carrier support of the assumed unknown source with extremely few discrete (possibly nonuniform) measurements taken on such an open set over a wide range of regularity classes of the source. Finally, we provide a few numerical examples which illustrate the efficacy and robustness of this location and tracking method.