Geodesic
Overdetermined parabolic boundary-value problems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 10, Tome 69 (1977), pp. 240-272

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The concept of an overdetermined, linear, parabolic system of differential equations of arbitrary order is introduced, and a theory of general over-determined, parabolic boundary-value problems in compact and noncompact domains with smooth boundaries is developed. 
@article{ZNSL_1977_69_a16,
     author = {A. G. Khachatryan},
     title = {Overdetermined parabolic boundary-value problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {240--272},
     publisher = {mathdoc},
     volume = {69},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_69_a16/}
}
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A. G. Khachatryan. Overdetermined parabolic boundary-value problems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 10, Tome 69 (1977), pp. 240-272. http://geodesic.mathdoc.fr/item/ZNSL_1977_69_a16/