Affiliation:
1. School of Mathematics and Statistics, Xiamen University of Technology, Xiamen, Fujian , China
Abstract
The paper follows with interest in a nonlinear parabolic equation coming from
the electrorheological fluid ut = div(a(x)|?u|p(x)?2?u) + ?N i=1 ?bi(u, x,
t)/ ?xi with a(x) being positive in ?. We study the well-posedness problem of
the equation under the condition bi(?, x, t) = 0 on the partial boundary ??
\ ?1 for every i = 1, 2,...,N, where ?1 = {x ? ?? : a(x) > 0}. The
stability of the weak solutions is obtained only basing on a partial
boundary value condition u(x, t) = 0, (x, t) ? ?1 ? (0, T).
Publisher
National Library of Serbia
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