Geodesic
On a heat propagation problem in a system of rods on a tree graph
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 89-95

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This paper is devoted to mathematical modeling of heat transfer in a system of rods on a tree graph by a pencil of linear differential operators. We examine the monotonic dependence of eigenvalues of the operator pencil on the parameters of boundary conditions. The problem is reduced to an inverse spectral problem for operators in a finite-dimensional spaces and a numerical solution algorithm for this problem is proposed.
Keywords: pencil of differential operators, inverse spectral problem, geometric graph. 
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     author = {Yu. V. Martynova},
     title = {On a heat propagation problem in a system of rods on a tree graph},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {89--95},
     publisher = {mathdoc},
     volume = {198},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_198_a9/}
}
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Yu. V. Martynova. On a heat propagation problem in a system of rods on a tree graph. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 89-95. http://geodesic.mathdoc.fr/item/INTO_2021_198_a9/