Abstract
The steady state non-Newtonian flow, with strain rate dependent viscosity in a thin tube structure, with no slip boundary condition, is considered. Applying the Banach fixed point theorem we prove the existence and uniqueness of a solution. An asymptotic approximation is constructed and justified by an error estimate.
Highlights
The asymptotic behavior of solutions of partial differential equations in thin domains is extensively studied in a vast mathematical literature
Viscous flows were studied in such domains and for the steady state Navier-Stokes equations an asymptotic expansion of the solution was constructed
The paper considers the stationary non-Newtonian Stokes system of equations in a thin tube structure modeling a network of blood vessels with the no slip boundary condition
Summary
The asymptotic behavior of solutions of partial differential equations in thin domains is extensively studied in a vast mathematical literature. The leading term of asymptotic expansion of the pressure is described by a one-dimensional elliptic non-linear problem on the graph. One-dimensional models derived from the conservation laws were introduced in [7]. These models differ from the problem on the graph: they are equations of hyperbolic type. By Wm,p(G) we denote the closure of the set C0∞(G) in the norm · W m,p(G), where C0∞(G) is the set of all infinitely differentiable functions with compact supports in G. More information about these spaces can be found in [1]. More specific functions spaces are introduced in places where they are used
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