STEADY FLOW OF FLUIDS WITH SHEAR-DEPENDENT VISCOSITY UNDER MIXED BOUNDARY VALUE CONDITIONS IN POLYHEDRAL DOMAINS

2000 ◽  
Vol 10 (05) ◽  
pp. 629-650 ◽  
Author(s):  
C. EBMEYER

In this paper the system of partial differential equations [Formula: see text] is studied, where e is the symmetrized gradient of u, and T has p-structure for some p<2 (e.g. div T is the p-Laplacian and p<2). Mixed boundary value conditions on a three-dimensional polyhedral domain are considered. Ws,p-regularity (s=3/2-ε) of the velocity u and Wr,p′-regularity of the pressure π are proven.

1950 ◽  
Vol 17 (4) ◽  
pp. 377-380
Author(s):  
R. D. Mindlin ◽  
L. E. Goodman

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.


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