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Some noncoercive parabolic equations with lower order terms in divergence form

Some noncoercive parabolic equations with lower order terms in divergence form This paper deals with existence and regularity results for the problem $ \cases{u_t-\mathrm{div}(a(x,t,u )\nabla u)=-\mathrm{div}(u\,E) \qquad in \Omega\times (0,T),\cr u=0 \qquad on \partial \Omega\times (0,T), \cr u (0)= u_0 \qquad in \Omega ,\cr} $ under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of the term div( uE ), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (\Omega)) $. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Some noncoercive parabolic equations with lower order terms in divergence form

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Birkhäuser-Verlag Basel
Subject
Mathematics
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-003-0109-7
Publisher site
See Article on Publisher Site

Abstract

This paper deals with existence and regularity results for the problem $ \cases{u_t-\mathrm{div}(a(x,t,u )\nabla u)=-\mathrm{div}(u\,E) \qquad in \Omega\times (0,T),\cr u=0 \qquad on \partial \Omega\times (0,T), \cr u (0)= u_0 \qquad in \Omega ,\cr} $ under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of the term div( uE ), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (\Omega)) $.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Aug 1, 2003

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