Geodesic
The heat equation on matrix space
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 268-285

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The analog of the heat equation on space of real matrixes was studied. On the basis of properties of the heat source the solution of the heat equation with initial radiation which defined in vertex of the cone of positive definite symmetrical matrixes was constructed. The correlations between the Riesz potentials associated with composite power functions on matrix space and solutions of the heat equation were found. 
@article{ZNSL_2006_332_a15,
     author = {S. P. Khekalo},
     title = {The heat equation on matrix space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {268--285},
     publisher = {mathdoc},
     volume = {332},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a15/}
}
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S. P. Khekalo. The heat equation on matrix space. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 268-285. http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a15/