The solution of an initial-boundary value problem of the filtration theory with nonlocal boundary condition - Serbina, Ludmila (Nonlinear Analysis: Modelling and Control, 2014)
The nonlocal initial and boundary value problem for Lavrentiev–Bitsadze equation is considered. By this problem the nonstacionary one-dimentional motion of a groundwater with horizontal stopping is modeling. The existence and the uniqueness of the classical (in the elliptic part of the domain) and generalized (in the hyperbolic part of the domain) solution of the considered problem is proved.
Keywords: motion of groundwater; Boussinesq's equation; equations of mixed type; Lavrentiev– Bitsadze equation; nonlocal problems; Samarskii condition; initial and boundary value problems