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Article overview
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Existence and asymptotic behavior of nontrivial solutions to the Swift-Hohenberg equation | Greta Marino
; Sunra Mosconi
; | Date: |
1 Sep 2016 | Abstract: | In this paper, we discuss several results regarding existence, non-existence
and asymptotic properties of solutions to $u""+qu"+f(u)=0$, under various
hypotheses on the parameter $q$ and on the potential $F(t)=int_0^tf(s), ds$,
generally assumed to be bounded from below. We prove a non-existence result in
the case $qle 0$ and an existence result of periodic solution for: 1) almost
every suitably small (depending on $F$), positive values of $q$; 2) all
suitably large (depending on $F$) values of $q$. Finally, we describe some
conditions on $F$ which ensure that some (or all) solutions $u_q$ to the
equation satisfy $|u_q|_infty o 0$, as $qdownarrow 0$. | Source: | arXiv, 1609.0179 | Services: | Forum | Review | PDF | Favorites |
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