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.


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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