Geodesic
Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 38-51

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Traditionally, absorbing boundary conditions are used to limit the domains of numerical approximation of partial differential equations in infinite domains. In the present paper, the simplest of these conditions is used to obtain an analytical approximation of the solution to the problem of heat propagation in a one-dimensional infinite harmonic lattice consisting of two semi-infinite homogeneous sublattices with different mechanical characteristics. 
@article{DVMG_2020_20_1_a3,
     author = {A. I. Gudimenko},
     title = {Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {38--51},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a3/}
}
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A. I. Gudimenko. Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 38-51. http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a3/