{"id":"https://openalex.org/W4224322524","doi":"https://doi.org/10.3390/sym14050861","title":"Lie Symmetries and Conservation Laws for the Viscous Cahn-Hilliard Equation","display_name":"Lie Symmetries and Conservation Laws for the Viscous Cahn-Hilliard Equation","publication_year":2022,"publication_date":"2022-04-22","ids":{"openalex":"https://openalex.org/W4224322524","doi":"https://doi.org/10.3390/sym14050861"},"language":"en","primary_location":{"id":"doi:10.3390/sym14050861","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14050861","pdf_url":"https://www.mdpi.com/2073-8994/14/5/861/pdf?version=1653361910","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/5/861/pdf?version=1653361910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040321437","display_name":"Almudena P. M\u00e1rquez","orcid":"https://orcid.org/0000-0001-7067-4906"},"institutions":[{"id":"https://openalex.org/I39147953","display_name":"Universidad de C\u00e1diz","ror":"https://ror.org/04mxxkb11","country_code":"ES","type":"education","lineage":["https://openalex.org/I39147953"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Almudena P. M\u00e1rquez","raw_affiliation_strings":["Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain"],"raw_orcid":"https://orcid.org/0000-0001-7067-4906","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain","institution_ids":["https://openalex.org/I39147953"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072102331","display_name":"Elena Recio","orcid":"https://orcid.org/0000-0001-6630-4574"},"institutions":[{"id":"https://openalex.org/I39147953","display_name":"Universidad de C\u00e1diz","ror":"https://ror.org/04mxxkb11","country_code":"ES","type":"education","lineage":["https://openalex.org/I39147953"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Elena Recio","raw_affiliation_strings":["Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain"],"raw_orcid":"https://orcid.org/0000-0001-6630-4574","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain","institution_ids":["https://openalex.org/I39147953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040735583","display_name":"M.L. Gandarias","orcid":"https://orcid.org/0000-0001-8604-8272"},"institutions":[{"id":"https://openalex.org/I39147953","display_name":"Universidad de C\u00e1diz","ror":"https://ror.org/04mxxkb11","country_code":"ES","type":"education","lineage":["https://openalex.org/I39147953"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u00eda L. Gandarias","raw_affiliation_strings":["Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8604-8272","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain","institution_ids":["https://openalex.org/I39147953"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040321437"],"corresponding_institution_ids":["https://openalex.org/I39147953"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2504,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48858424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"14","issue":"5","first_page":"861","last_page":"861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9570000171661377,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.9049307107925415},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7589794993400574},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.7045308947563171},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.5735421776771545},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5566883683204651},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.47024860978126526},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.46430590748786926},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4544511139392853},{"id":"https://openalex.org/keywords/spacetime-symmetries","display_name":"Spacetime symmetries","score":0.4459371566772461},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3858301639556885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3721265494823456},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.34718188643455505},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30017992854118347},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.09684139490127563}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.9049307107925415},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7589794993400574},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7045308947563171},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.5735421776771545},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5566883683204651},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47024860978126526},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.46430590748786926},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4544511139392853},{"id":"https://openalex.org/C65305961","wikidata":"https://www.wikidata.org/wiki/Q7572737","display_name":"Spacetime symmetries","level":5,"score":0.4459371566772461},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3858301639556885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3721265494823456},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.34718188643455505},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30017992854118347},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.09684139490127563},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C120484201","wikidata":"https://www.wikidata.org/wiki/Q2246697","display_name":"Quantum field theory in curved spacetime","level":4,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14050861","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14050861","pdf_url":"https://www.mdpi.com/2073-8994/14/5/861/pdf?version=1653361910","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4aadee5fbfbf4c3b9dd8c499d4aca939","is_oa":true,"landing_page_url":"https://doaj.org/article/4aadee5fbfbf4c3b9dd8c499d4aca939","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 5, p 861 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/861/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14050861","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"},{"id":"pmh:oai:rodin.uca.es:10498/27199","is_oa":true,"landing_page_url":"http://hdl.handle.net/10498/27199","pdf_url":null,"source":{"id":"https://openalex.org/S4306400506","display_name":"RODIN (Universidad de C\u00e1diz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39147953","host_organization_name":"Universidad de C\u00e1diz","host_organization_lineage":["https://openalex.org/I39147953"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol. 14, N\u00fam. 5","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/sym14050861","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14050861","pdf_url":"https://www.mdpi.com/2073-8994/14/5/861/pdf?version=1653361910","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.7300000190734863,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G809214183","display_name":null,"funder_award_id":"FQM-201","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"}],"funders":[{"id":"https://openalex.org/F4320325313","display_name":"Universidad de C\u00e1diz","ror":"https://ror.org/04mxxkb11"},{"id":"https://openalex.org/F4320326754","display_name":"Junta de Andaluc\u00eda","ror":"https://ror.org/01jem9c82"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4224322524.pdf","grobid_xml":"https://content.openalex.org/works/W4224322524.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1506397612","https://openalex.org/W1541425020","https://openalex.org/W2005965954","https://openalex.org/W2007822838","https://openalex.org/W2034063402","https://openalex.org/W2037654468","https://openalex.org/W2046528357","https://openalex.org/W2048446124","https://openalex.org/W2051959080","https://openalex.org/W2062561585","https://openalex.org/W2081281136","https://openalex.org/W2082921691","https://openalex.org/W2085493421","https://openalex.org/W2171170318","https://openalex.org/W2404293814","https://openalex.org/W2794062217","https://openalex.org/W2797256054","https://openalex.org/W2963371262","https://openalex.org/W2996088060","https://openalex.org/W3022230513","https://openalex.org/W3034915735","https://openalex.org/W3036368930","https://openalex.org/W3197065098","https://openalex.org/W4229672964","https://openalex.org/W6652443389"],"related_works":["https://openalex.org/W2044789371","https://openalex.org/W2056464752","https://openalex.org/W1993566193","https://openalex.org/W2117461150","https://openalex.org/W2029211066","https://openalex.org/W2373595193","https://openalex.org/W4361230636","https://openalex.org/W2154208118","https://openalex.org/W3207893191","https://openalex.org/W3200654568"],"abstract_inverted_index":{"In":[0,61],"this":[1,24],"paper,":[2],"we":[3,97,109,121],"study":[4],"a":[5,35,49,132],"viscous":[6],"Cahn\u2013Hilliard":[7],"equation":[8,25,58,73,129],"from":[9],"the":[10,52,57,63,70,93,123,128],"point":[11],"of":[12,14,23,51],"view":[13],"Lie":[15,53],"symmetries":[16,54,115],"in":[17,40],"partial":[18,71],"differential":[19,72,78],"equations.":[20],"The":[21],"analysis":[22],"is":[26,59,74],"motivated":[27],"by":[28,56,91],"its":[29],"applications":[30],"since":[31],"it":[32],"serves":[33],"as":[34],"model":[36],"for":[37],"many":[38],"problems":[39],"physical":[41],"chemistry,":[42],"developmental":[43],"biology,":[44],"and":[45,108,116,130],"population":[46],"movement.":[47],"Firstly,":[48],"classification":[50],"admitted":[55],"presented.":[60],"addition,":[62],"symmetry":[64,81],"transformation":[65],"groups":[66],"are":[67,89],"calculated.":[68],"Afterwards,":[69],"transformed":[75],"into":[76],"ordinary":[77],"equations":[79],"through":[80],"reductions.":[82],"Secondly,":[83],"all":[84],"low-order":[85],"local":[86],"conservation":[87,100,118],"laws":[88,101],"obtained":[90],"using":[92],"multiplier":[94],"method.":[95],"Furthermore,":[96],"use":[98,110],"these":[99],"to":[102,112,126],"determine":[103],"their":[104],"associated":[105],"potential":[106],"systems":[107],"them":[111],"investigate":[113],"nonlocal":[114,117],"laws.":[119],"Finally,":[120],"apply":[122],"multi-reduction":[124],"method":[125],"reduce":[127],"find":[131],"soliton":[133],"solution.":[134]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-04-26T00:00:00"}
