Upper and lower bounds for the speed of fronts of the reaction diffusion equation with Stefan boundary conditions
We establish two integral variational principles for the spreading speed of the one dimensional reaction diffusion equation with Stefan boundary conditions. The first principle is valid for monostable reaction terms and the second principle is valid for arbitrary reaction terms. These principles all...
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| description | We establish two integral variational principles for the spreading speed of the one dimensional reaction diffusion equation with Stefan boundary conditions. The first principle is valid for monostable reaction terms and the second principle is valid for arbitrary reaction terms. These principles allow to obtain several upper and lower bounds for the speed. In particular, we construct a generalized Zeldovich-Frank-Kamenetskii type lower bound for the speed and upper bounds in terms of the speed of the standard reaction diffusion problem. We construct asymptotically exact lower bounds previously obtained by perturbation theory. |
| doi_str_mv | 10.48550/arxiv.1910.11695 |
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The first principle is valid for monostable reaction terms and the second principle is valid for arbitrary reaction terms. These principles allow to obtain several upper and lower bounds for the speed. In particular, we construct a generalized Zeldovich-Frank-Kamenetskii type lower bound for the speed and upper bounds in terms of the speed of the standard reaction diffusion problem. We construct asymptotically exact lower bounds previously obtained by perturbation theory.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1910.11695</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Boundary conditions ; Diffusion rate ; First principles ; Lower bounds ; Mathematics - Analysis of PDEs ; Mathematics - Mathematical Physics ; Perturbation theory ; Physics - Mathematical Physics ; Reaction-diffusion equations ; Upper bounds ; Variational principles</subject><ispartof>arXiv.org, 2022-08</ispartof><rights>2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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We construct asymptotically exact lower bounds previously obtained by perturbation theory.</description><subject>Boundary conditions</subject><subject>Diffusion rate</subject><subject>First principles</subject><subject>Lower bounds</subject><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Mathematical Physics</subject><subject>Perturbation theory</subject><subject>Physics - Mathematical Physics</subject><subject>Reaction-diffusion equations</subject><subject>Upper bounds</subject><subject>Variational principles</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotUMtqwzAQFIVCQ5oP6KmCnp3q4bWtYwl9BAI9ND0b2VoRh1RyJLtp_75y0tMMs8OwM4TccbbMKwD2qMNP973kKgmcFwquyExIybMqF-KGLGLcM8ZEUQoAOSPHz77HQLUz9OBPiTV-dCZS6wMddkhjj2iot9QG74Y4sUkOqNuh846aztoxTgyPoz5Lp27Y0Y8BrXaXNB1-aeud6aZzvCXXVh8iLv5xTrYvz9vVW7Z5f12vnjaZVgCZQZEzDsgVtFXeVK2EptTWgC5tDq0AayouSxBNKqoQpNFYJSgUT0WhkHNyf4k971H3oftKf9TTLvV5l-R4uDj64I8jxqHe-zG49FMtJFNQlMkk_wAarGbb</recordid><startdate>20220822</startdate><enddate>20220822</enddate><creator>Benguria, R D</creator><creator>Depassier, M C</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220822</creationdate><title>Upper and lower bounds for the speed of fronts of the reaction diffusion equation with Stefan boundary conditions</title><author>Benguria, R D ; Depassier, M C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a955-de24015e195c84b8c35b7afd5a7f45c25fd813752b9109e53dae8e53691842563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Boundary conditions</topic><topic>Diffusion rate</topic><topic>First principles</topic><topic>Lower bounds</topic><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Mathematical Physics</topic><topic>Perturbation theory</topic><topic>Physics - Mathematical Physics</topic><topic>Reaction-diffusion equations</topic><topic>Upper bounds</topic><topic>Variational principles</topic><toplevel>online_resources</toplevel><creatorcontrib>Benguria, R D</creatorcontrib><creatorcontrib>Depassier, M C</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Benguria, R D</au><au>Depassier, M C</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Upper and lower bounds for the speed of fronts of the reaction diffusion equation with Stefan boundary conditions</atitle><jtitle>arXiv.org</jtitle><date>2022-08-22</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>We establish two integral variational principles for the spreading speed of the one dimensional reaction diffusion equation with Stefan boundary conditions. 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| subjects | Boundary conditions Diffusion rate First principles Lower bounds Mathematics - Analysis of PDEs Mathematics - Mathematical Physics Perturbation theory Physics - Mathematical Physics Reaction-diffusion equations Upper bounds Variational principles |
| title | Upper and lower bounds for the speed of fronts of the reaction diffusion equation with Stefan boundary conditions |
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