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**Boundary value problem for the Aller-Lykov moisture transport generalized equation with concentrated heat capacity.**
*(Russian.
English summary)*
Zbl 1427.35276

Summary: The article considers the Aller-Lykov equation with a Riemann-Liouville fractional time derivative, boundary conditions of the third kind and with the concentrated specific heat capacity on the boundary of the domain. Similar conditions arise in the case with a material of a higher thermal conductivity when solving a temperature problem for restricted environment with a heater as a concentrated heat capacity. Analogous conditions also arise in practices for regulating the water-salt regime of soils, when desalination of the upper layer is achieved by draining of a surface of the flooded for a while area. Using energy inequality methods, we obtained an a priori estimate in terms of the Riemann-Liouville fractional derivative, which revealed the uniqueness of the solution to the problem under consideration.

### MSC:

35Q79 | PDEs in connection with classical thermodynamics and heat transfer |

35R11 | Fractional partial differential equations |

35K05 | Heat equation |

35J25 | Boundary value problems for second-order elliptic equations |

### Keywords:

Aller-Lykov equation; fractional derivative; nonlocal problem; moisture transfer generalized equation; concentrated heat capacity; inequalities method; a priori estimate; boundary value problem
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\textit{M. A. Kerefov} et al., Vestn. Samar. Univ., Estestvennonauchn. Ser. 24, No. 3, 23--29 (2018; Zbl 1427.35276)

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