Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
19 (1996), S. 991-1015
ISSN:
0170-4214
Keywords:
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We study a quasi-static incompressible flow of Bingham type with constituent law\[ \begin{array}{ll} T = p\left| {\cal E}u\right| ⁁{p-2}{\cal E}u+\beta \frac{{\cal E}u}{\left| {\cal E}u\right| } & \text{if }{\cal E}u\neq 0, \\ \left| T\right| \leq \beta & \text{if }{\cal E}u = 0, \end{array} \] T = p∣Eu∣p-2Eu+β Eu ∣Eu∣ if Eu≠0,∣T∣≤β if Eu = 0, where p≥2 and β〉0. Here Eu denotes the strain velocity and T the corresponding stress. The problem admits a variational formulation in the sense that the velocity field u minimizes the energy I(u) = ∫Ω∣Eu∣p+β∣Eu∣dx in the space {v∊H1,p(Ω,∝n): div v = 0} subject to appropriate boundary conditions. We then show smoothness of u on the set {x∊Ω: Eu≠0}.
Type of Medium:
Electronic Resource
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