On a third order initial boundary value problem in a plane domain - Klovienė, Neringa (Nonlinear Analysis: Modelling and Control, 2012)
Third order initial boundary value problem is studied in a bounded plane domain σ with C4 smooth boundary ∂σ. The existence and uniqueness of the solution is proved using Galerkin approximations and a priory estimates. The problem under consideration appear as an auxiliary problem by studying a second grade fluid motion in an infinite three-dimensional pipe with noncircular cross-section.
Keywords: initial boundary value problem; third order evolutionary equation; second grade fluid flow; infinite pipe flow