On the solution of a hyperbolic one-dimensional free boundary problem for a Maxwell fluid
Summary: We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of the authors [Far East J. Appl. Math. 52, No. 1, 43--80 (2011; Zbl 1230.35146)]. The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.
scientific article; zbMATH DE number 6012966