{"id":"https://openalex.org/W4401097293","doi":"https://doi.org/10.1137/23m1591803","title":"A Geometric Singular Perturbation Analysis of Shock Selection Rules in Composite Regularized Reaction-Nonlinear Diffusion Models","display_name":"A Geometric Singular Perturbation Analysis of Shock Selection Rules in Composite Regularized Reaction-Nonlinear Diffusion Models","publication_year":2024,"publication_date":"2024-07-29","ids":{"openalex":"https://openalex.org/W4401097293","doi":"https://doi.org/10.1137/23m1591803"},"language":"en","primary_location":{"id":"doi:10.1137/23m1591803","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1591803","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032072994","display_name":"Bronwyn H. Bradshaw\u2010Hajek","orcid":"https://orcid.org/0000-0002-7892-4620"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Bronwyn H. Bradshaw-Hajek","raw_affiliation_strings":["UniSA STEM, University of South Australia, Mawson Lakes, South Australia, Australia"],"affiliations":[{"raw_affiliation_string":"UniSA STEM, University of South Australia, Mawson Lakes, South Australia, Australia","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080683556","display_name":"Ian Lizarraga","orcid":"https://orcid.org/0000-0001-9680-1491"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ian Lizarraga","raw_affiliation_strings":["School of Mathematics and Statistics, University of Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075367134","display_name":"Robert Marangell","orcid":"https://orcid.org/0000-0003-0543-162X"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Robert Marangell","raw_affiliation_strings":["School of Mathematics and Statistics, University of Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089288259","display_name":"Martin Wechselberger","orcid":"https://orcid.org/0000-0003-2681-3440"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Martin Wechselberger","raw_affiliation_strings":["School of Mathematics and Statistics, University of Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032072994"],"corresponding_institution_ids":["https://openalex.org/I170239107"],"apc_list":null,"apc_paid":null,"fwci":3.902,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.93475945,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"23","issue":"3","first_page":"2099","last_page":"2137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.734798789024353},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6952434778213501},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5481085181236267},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.5104290843009949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4949635863304138},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.48693764209747314},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4435686469078064},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38759276270866394},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3570491671562195},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33280256390571594},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2039145827293396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09302303194999695}],"concepts":[{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.734798789024353},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6952434778213501},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5481085181236267},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.5104290843009949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4949635863304138},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.48693764209747314},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4435686469078064},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38759276270866394},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3570491671562195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33280256390571594},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2039145827293396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09302303194999695},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1591803","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1591803","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:urm_publish:9916888330501831","is_oa":false,"landing_page_url":"https://find.library.unisa.edu.au/discovery/fulldisplay/alma9916888330501831/61USOUTHAUS_INST:ROR","pdf_url":null,"source":{"id":"https://openalex.org/S4306402528","display_name":"UniSA Research Outputs Repository (University of South Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170239107","host_organization_name":"University of South Australia","host_organization_lineage":["https://openalex.org/I170239107"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","id":"https://metadata.un.org/sdg/13","score":0.8299999833106995}],"awards":[{"id":"https://openalex.org/G6605748703","display_name":null,"funder_award_id":"DP200102130","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1484182740","https://openalex.org/W1733231289","https://openalex.org/W1930920613","https://openalex.org/W1968181774","https://openalex.org/W1968468027","https://openalex.org/W1970717294","https://openalex.org/W1972135589","https://openalex.org/W1992737652","https://openalex.org/W1996099237","https://openalex.org/W1999873750","https://openalex.org/W2018907418","https://openalex.org/W2034879619","https://openalex.org/W2042401506","https://openalex.org/W2059479894","https://openalex.org/W2063827672","https://openalex.org/W2079949023","https://openalex.org/W2093823001","https://openalex.org/W2094098398","https://openalex.org/W2097429676","https://openalex.org/W2120732869","https://openalex.org/W2130218155","https://openalex.org/W2158547124","https://openalex.org/W2569713119","https://openalex.org/W2951140671","https://openalex.org/W3008606610","https://openalex.org/W3017711825","https://openalex.org/W3042436329","https://openalex.org/W3155531438","https://openalex.org/W4213388037","https://openalex.org/W4237997615","https://openalex.org/W4254352406","https://openalex.org/W4384339307","https://openalex.org/W4391188497"],"related_works":["https://openalex.org/W2055379029","https://openalex.org/W4205762803","https://openalex.org/W2011339542","https://openalex.org/W4327639758","https://openalex.org/W2119556180","https://openalex.org/W2116787190","https://openalex.org/W2154304710","https://openalex.org/W2623488306","https://openalex.org/W1971902905","https://openalex.org/W2006371715"],"abstract_inverted_index":{"Reaction-nonlinear":[0],"diffusion":[1],"partial":[2],"differential":[3],"equations":[4],"(RND":[5],"PDEs)":[6],"have":[7],"recently":[8],"been":[9],"developed":[10],"as":[11,43,85,236,238],"a":[12,44,65,86,186,256],"powerful":[13],"and":[14,29,39,50,304,314],"flexible":[15],"modeling":[16],"tool":[17],"in":[18,27,57,136,244,287,301,339],"order":[19],"to":[20,46,88,102,105,115,156,196,203,334],"investigate":[21,47],"the":[22,37,48,95,122,137,190,204,209,245,281,288,299,327,340,344],"emergence":[23],"of":[24,41,52,108,159,189,208,261,263,298,326,343],"steep":[25],"fronts":[26],"biological":[28],"ecological":[30],"contexts.":[31],"In":[32,64,140],"this":[33,141],"work,":[34,142],"we":[35,143],"demonstrate":[36,219],"utility":[38],"scope":[40],"regularization":[42],"technique":[45],"existence":[49,253],"uniqueness":[51],"steep-fronted":[53,110,267],"traveling":[54,111,162,205],"wave":[55,206],"solutions":[56],"RND":[58,92,211,330],"PDE":[59,331],"models":[60],"with":[61,255],"forward-backward-forward":[62],"diffusion.":[63],"recent":[66,293],"work":[67],"(see":[68],"[Y.":[69],"Li":[70],"et":[71],"al.,":[72],"Phys.":[73,307],"D,":[74,308],"423":[75],"(2021),":[76],"132916]),":[77],"geometric":[78,272],"singular":[79,118],"perturbation":[80],"theory":[81],"(GSPT)":[82],"was":[83],"introduced":[84],"framework":[87],"analyze":[89],"these":[90,174,252,264],"regularized":[91,210,329],"PDEs.":[93],"Using":[94,269],"GSPT":[96,200],"toolbox,":[97],"different":[98],"regularizations":[99,152],"were":[100],"shown":[101],"give":[103],"rise":[104],"distinct":[106,166,214],"families":[107,158,283],"monotone":[109,160,282],"waves":[112,163,235,240],"which":[113,170,192,291],"limit":[114],"their":[116],"shock-fronted":[117,161,230,234,239],"counterparts,":[119],"obeying":[120],"either":[121],"equal":[123],"area":[124,127,168],"or":[125],"extremal":[126,176],"(i.e.,":[128],"algebraic":[129],"decay)":[130],"rules":[131,177],"that":[132,150,223,280],"are":[133],"well":[134,237],"known":[135],"shockwave":[138],"literature.":[139],"extend":[144],"those":[145],"earlier":[146],"results":[147,254,278,295],"by":[148,296],"showing":[149],"composite":[151,225,328],"can":[153,193],"be":[154,194],"used":[155],"construct":[157],"sweeping":[164],"out":[165],"generalized":[167],"rules,":[169],"smoothly":[171],"interpolate":[172],"between":[173],"two":[175],"for":[178],"shock":[179],"selection.":[180],"Our":[181],"analysis":[182,260,342],"blends":[183],"Melnikov":[184],"methods\u2014including":[185],"new":[187,265],"variant":[188],"method":[191],"applied":[195,202],"autonomous":[197],"piecewise-smooth":[198],"systems\u2014with":[199],"techniques":[201,270],"problem":[207],"model":[212,226,332],"over":[213],"spatiotemporal":[215],"scales.":[216],"We":[217,250],"further":[218],"using":[220],"numerical":[221,257,277,341],"continuation":[222],"our":[224,276],"supports":[227],"more":[228],"exotic":[229],"solutions,":[231],"namely,":[232],"nonmonotone":[233],"containing":[241],"slow":[242],"tails":[243],"aggregation":[246],"(backward":[247],"diffusion)":[248],"regime.":[249],"complement":[251],"spectral":[258,273],"stability":[259,274,294],"some":[262,297],"\u201cinterpolated\u201d":[266],"waves.":[268],"from":[271],"theory,":[275],"suggest":[279],"remain":[284],"spectrally":[285],"stable":[286],"\u201cinterpolation\u201d":[289],"regime,":[290],"extends":[292],"authors":[300],"[I.":[302,312],"Lizarraga":[303,313],"R.":[305,315],"Marangell,":[306,316],"460":[309],"(2024),":[310],"134069],":[311],"J.":[317],"Nonlinear":[318],"Sci.,":[319],"33":[320],"(2023),":[321],"82].":[322],"The":[323],"multiple-scale":[324],"nature":[325],"continues":[333],"play":[335],"an":[336],"important":[337],"role":[338],"spatial":[345],"eigenvalue":[346],"problem.":[347]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2024-07-31T00:00:00"}
