STABILITY PROPERTIES OF PARABOLIC EQUATIONS IN UNBOUNDED-DOMAINS

Authors
ESCHER J SCARPELLINI B
Citation
J. Escher et B. Scarpellini, STABILITY PROPERTIES OF PARABOLIC EQUATIONS IN UNBOUNDED-DOMAINS, Archiv der Mathematik, 71(1), 1998, pp. 31-45
Citations number
18
Categorie Soggetti
Mathematics,Mathematics
Journal title
Archiv der Mathematik → ACNP
ISSN journal
0003889X
Volume
71
Issue
1
Year of publication
1998
Pages
31 - 45
Database
ISI
SICI code
0003-889X(1998)71:1<31:SPOPEI>2.0.ZU;2-O
Abstract
We consider semilinear parabolic equations on unbounded domains in IR2 or IR3 with forcing polynomial nonlinearities of the form g(u) = au(p ) + bup(p+1) + ... with a > 0 and p greater than or equal to 2. It is shown that the zero solution of the induced semiflow is positively uns table, provided p = 2 and the domain contains arbitrarily large sphere s. If p > 2 and if g possesses a positive root, then the zero solution is positively stable.