2002
DOI: 10.1006/jdeq.2001.4018
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Remarks on Third-Order ODEs Relevant to the Kuramoto–Sivashinsky Equation

Abstract: dedicated to professor hiroko morimoto on her jubileeWe are interested in the third-order ordinary differential equations (ODEs) which are related to the Kuramoto-Sivashinsky equation. So-called steady solutions of the Kuramoto-Sivashinsky equation are known to admit several types; for example, bounded global solutions or periodic solutions. We show that, in addition to these, there exist solutions which blow up on bounded intervals. Moreover, for certain classes of these ODEs, the nonexistence of nontrivial b… Show more

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Cited by 3 publications
(2 citation statements)
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“…The above family plays a very relevant role in the study of the KuramotoShivashinsky equation u t þ u xxxx þ u xx þ 1 2 u 2 x ¼ 0; namely, in relation with the existence of steady solutions and travelling waves (see, for instance, [7,9,10] and references therein). Along the paper we will write family (4) either as…”
Section: Introductionmentioning
confidence: 99%
“…The above family plays a very relevant role in the study of the KuramotoShivashinsky equation u t þ u xxxx þ u xx þ 1 2 u 2 x ¼ 0; namely, in relation with the existence of steady solutions and travelling waves (see, for instance, [7,9,10] and references therein). Along the paper we will write family (4) either as…”
Section: Introductionmentioning
confidence: 99%
“…This technique itself has been known already [9], and employed in various other papers [1], [2], [3], [7] and [8]; we present the utility of the method in combination with numerical treatment.…”
Section: Introductionmentioning
confidence: 99%