Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities

dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.contributor.authorGiletti, Thomas
dc.contributor.authorKim, Ho Youn
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.institutionInstitut Elie Cartan de Lorraine, UMR 7502, University of Lorraine, 54506, Vandoeuvre-les-Nancy, France
dc.date.accessioned2023-07-16T10:41:33Z
dc.date.available2023-01-31T11:17:52Z
dc.date.available2023-07-16T10:41:33Z
dc.date.issued2023-06-25
dc.description.abstractIn this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.
dc.description.sponsorshipThis work was carried out in the framework of the CNRS International Research Network “ReaDiNet”. The two authors were also supported by the joint PHC Star project MAP, France, funded by the French Ministry for Europe and Foreign Affairs and the National Research Foundation of Korea. The first author also acknowledges support from ANR, France via the project Indyana under grant agreement ANR- 21- CE40-0008.
dc.eprint.versionPre-print
dc.identifier.arxivid2207.14565
dc.identifier.citationGiletti, T., & Kim, H.-Y. (2023). Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities. Nonlinear Analysis: Real World Applications, 74, 103924. https://doi.org/10.1016/j.nonrwa.2023.103924
dc.identifier.doi10.1016/j.nonrwa.2023.103924
dc.identifier.eid2-s2.0-85163675971
dc.identifier.issn1468-1218
dc.identifier.journalNonlinear Analysis: Real World Applications
dc.identifier.pages103924
dc.identifier.urihttp://hdl.handle.net/10754/687422
dc.identifier.volume74
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S1468121823000949
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Real World Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Real World Applications, [74, , (2023-06-25)] DOI: 10.1016/j.nonrwa.2023.103924 . © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleConvergence to a terrace solution in multistable reaction–diffusion equation with discontinuities
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Giletti, Thomas,equals">Giletti, Thomas</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0003-1606-2671&spc.sf=dc.date.issued&spc.sd=DESC">Kim, Ho Youn</a> <a href="https://orcid.org/0000-0003-1606-2671" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia,equals">Computer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division</a><br><br><h5>Date</h5>2023-06-25</span>
display.details.right<span><h5>Abstract</h5>In this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.<br><br><h5>Citation</h5>Giletti, T., & Kim, H.-Y. (2023). Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities. Nonlinear Analysis: Real World Applications, 74, 103924. https://doi.org/10.1016/j.nonrwa.2023.103924<br><br><h5>Acknowledgements</h5>This work was carried out in the framework of the CNRS International Research Network “ReaDiNet”. The two authors were also supported by the joint PHC Star project MAP, France, funded by the French Ministry for Europe and Foreign Affairs and the National Research Foundation of Korea. The first author also acknowledges support from ANR, France via the project Indyana under grant agreement ANR- 21- CE40-0008.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Elsevier BV,equals">Elsevier BV</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Nonlinear Analysis: Real World Applications,equals">Nonlinear Analysis: Real World Applications</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1016/j.nonrwa.2023.103924">10.1016/j.nonrwa.2023.103924</a><br><br><h5>arXiv</h5><a href="https://arxiv.org/abs/2207.14565">2207.14565</a><br><br><h5>Additional Links</h5>https://linkinghub.elsevier.com/retrieve/pii/S1468121823000949</span>
kaust.personKim, Ho Youn
orcid.authorGiletti, Thomas
orcid.authorKim, Ho Youn::0000-0003-1606-2671
orcid.id0000-0003-1606-2671
pubs.publication-statusSubmitted
refterms.dateFOA2023-01-31T11:17:53Z
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