%0 Journal Article
%T On a nonstationary nonlinear coupled system
%A Li
%A Gang
%A Wang
%A Hui
%A Zhu
%A Jiang
%J Computational & Applied Mathematics
%D 2011
%I Scientific Electronic Library Online
%R 10.1590/S1807-03022011000300003
%X in this paper, a strongly nonlinear coupled elliptic-parabolic system modelling a class of engineering problems with heat effect is studied. existence of a weak solution is first established by schauder fixed point theorem, where the coupled functions ¦Ò(s), k(s) are assumed to be bounded. the uniqueness of the solution is obtained by applying meyers' theorem and assuming that ¦Ò(s), k(s) are lipschitz continuous. the regularity of the solution is then analyzed in dimension d < 2 under the assumptions on ¦Ò(s), k(s) ¡Ê c2(r) and the boundedness of their derivatives of second order. finally, the blow-up phenomena of the system are studied. mathematical subject classification: 35j60, 35k55.
%K elliptic-parabolic system
%K existence
%K uniqueness
%K regularity
%K blow-up.
%U http://www.scielo.br/scielo.php?script=sci_abstract&pid=S1807-03022011000300003&lng=en&nrm=iso&tlng=en