## 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
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