“…Heat conduction phenomena of material involving moving heat sources, which have attracted increasing attention by scientists and engineers in the past few decades, have been studied in a wide range of fields, such as welding, cutting, drilling, laser hardening/forming, plasma spraying, heat treating of metals, manufacturing of electronic components, and even firing a gun barrel, solid propellant burning, and dental treatment, see e.g., [1][2][3][4][5] and references therein. The most important physical quantity of interest for such practical applications is the temperature field of the medium, which is usually modeled by the heat conduction equation with time-dependent localized source terms for moving heat sources.…”