Geodesic
Autoregulated Impulse Point Heating of a~Finite Medium
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 102-106

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We consider a finite heat conducting medium whose boundary is maintained at zero temperature and, moreover, to which the same amount of heat is supplied at a certain point at the instant when the temperature at this point decreases to a given level. Up to an arbitrary shift in time, we prove the existence and uniqueness of a periodic regime with a unique heat pulse during each period. We present an efficient algorithm for constructing this regime if the medium is either an $n$-dimensional ball heated at the center or an interval heated at an arbitrary point. 
@article{MZM_2006_79_1_a7,
     author = {A. D. Myshkis},
     title = {Autoregulated {Impulse} {Point} {Heating} of {a~Finite} {Medium}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {102--106},
     publisher = {mathdoc},
     volume = {79},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a7/}
}
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A. D. Myshkis. Autoregulated Impulse Point Heating of a~Finite Medium. Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 102-106. http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a7/