Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W3035440551', 'doi': 'https://doi.org/10.1016/j.jde.2020.05.022', 'title': 'Inverse problems for heat equation and space–time fractional diffusion equation with one measurement', 'display_name': 'Inverse problems for heat equation and space–time fractional diffusion equation with one measurement', 'publication_year': 2020, 'publication_date': '2020-06-09', 'ids': {'openalex': 'https://openalex.org/W3035440551', 'doi': 'https://doi.org/10.1016/j.jde.2020.05.022', 'mag': '3035440551'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1016/j.jde.2020.05.022', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S200871675', 'display_name': 'Journal of Differential Equations', 'issn_l': '0022-0396', 'issn': ['0022-0396', '1090-2732'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/pdf/1903.04348', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5087514308', 'display_name': 'Tapio Helin', 'orcid': 'https://orcid.org/0000-0002-5788-0008'}, 'institutions': [{'id': 'https://openalex.org/I63548447', 'display_name': 'Lappeenranta-Lahti University of Technology', 'ror': 'https://ror.org/0208vgz68', 'country_code': 'FI', 'type': 'education', 'lineage': ['https://openalex.org/I63548447']}], 'countries': ['FI'], 'is_corresponding': False, 'raw_author_name': 'Tapio Helin', 'raw_affiliation_strings': ['School of Engineering Science, LUT University, Finland'], 'affiliations': [{'raw_affiliation_string': 'School of Engineering Science, LUT University, Finland', 'institution_ids': ['https://openalex.org/I63548447']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5052627284', 'display_name': 'Matti Lassas', 'orcid': 'https://orcid.org/0000-0003-2043-3156'}, 'institutions': [{'id': 'https://openalex.org/I1323065761', 'display_name': 'Statistics Finland', 'ror': 'https://ror.org/01n1rg855', 'country_code': 'FI', 'type': 'other', 'lineage': ['https://openalex.org/I1323065761']}, {'id': 'https://openalex.org/I133731052', 'display_name': 'University of Helsinki', 'ror': 'https://ror.org/040af2s02', 'country_code': 'FI', 'type': 'education', 'lineage': ['https://openalex.org/I133731052']}], 'countries': ['FI'], 'is_corresponding': True, 'raw_author_name': 'Matti Lassas', 'raw_affiliation_strings': ['Department of Mathematics and Statistics, University of Helsinki, Finland'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics and Statistics, University of Helsinki, Finland', 'institution_ids': ['https://openalex.org/I1323065761', 'https://openalex.org/I133731052']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5033210905', 'display_name': 'Lauri Ylinen', 'orcid': 'https://orcid.org/0000-0002-7520-6068'}, 'institutions': [{'id': 'https://openalex.org/I1323065761', 'display_name': 'Statistics Finland', 'ror': 'https://ror.org/01n1rg855', 'country_code': 'FI', 'type': 'other', 'lineage': ['https://openalex.org/I1323065761']}, {'id': 'https://openalex.org/I133731052', 'display_name': 'University of Helsinki', 'ror': 'https://ror.org/040af2s02', 'country_code': 'FI', 'type': 'education', 'lineage': ['https://openalex.org/I133731052']}], 'countries': ['FI'], 'is_corresponding': False, 'raw_author_name': 'Lauri Ylinen', 'raw_affiliation_strings': ['Department of Mathematics and Statistics, University of Helsinki, Finland'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics and Statistics, University of Helsinki, Finland', 'institution_ids': ['https://openalex.org/I1323065761', 'https://openalex.org/I133731052']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5006194809', 'display_name': 'Zhidong Zhang', 'orcid': 'https://orcid.org/0000-0003-0197-4889'}, 'institutions': [{'id': 'https://openalex.org/I157773358', 'display_name': 'Sun Yat-sen University', 'ror': 'https://ror.org/0064kty71', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I157773358']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Zhidong Zhang', 'raw_affiliation_strings': ['School of Mathematics (Zhuhai), Sun Yat-sen University, China'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematics (Zhuhai), Sun Yat-sen University, China', 'institution_ids': ['https://openalex.org/I157773358']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 4, 'corresponding_author_ids': ['https://openalex.org/A5052627284'], 'corresponding_institution_ids': ['https://openalex.org/I1323065761', 'https://openalex.org/I133731052'], 'apc_list': {'value': 2930, 'currency': 'USD', 'value_usd': 2930, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.455, 'has_fulltext': False, 'cited_by_count': 18, 'citation_normalized_percentile': {'value': 0.999815, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 92, 'max': 93}, 'biblio': {'volume': '269', 'issue': '9', 'first_page': '7498', 'last_page': '7528'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10288', 'display_name': 'Anomalous Diffusion Modeling and Analysis', 'score': 0.9997, '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'}}, 'topics': [{'id': 'https://openalex.org/T10288', 'display_name': 'Anomalous Diffusion Modeling and Analysis', 'score': 0.9997, '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'}}, {'id': 'https://openalex.org/T11205', 'display_name': 'Inverse Problems in Mathematical Physics and Imaging', 'score': 0.999, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, '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/T12100', 'display_name': 'Multiscale Methods for Heterogeneous Systems', 'score': 0.9943, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/riemannian-manifold', 'display_name': 'Riemannian manifold', 'score': 0.79563344}, {'id': 'https://openalex.org/keywords/heat-equation', 'display_name': 'Heat equation', 'score': 0.79172}, {'id': 'https://openalex.org/keywords/time-fractional-diffusion-equation', 'display_name': 'Time-Fractional Diffusion Equation', 'score': 0.614963}, {'id': 'https://openalex.org/keywords/manifold', 'display_name': 'Manifold (fluid mechanics)', 'score': 0.59513485}, {'id': 'https://openalex.org/keywords/inverse-problems', 'display_name': 'Inverse Problems', 'score': 0.518607}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.79673505}, {'id': 'https://openalex.org/C2779593128', 'wikidata': 'https://www.wikidata.org/wiki/Q632814', 'display_name': 'Riemannian manifold', 'level': 2, 'score': 0.79563344}, {'id': 'https://openalex.org/C202787564', 'wikidata': 'https://www.wikidata.org/wiki/Q6510488', 'display_name': 'Heat equation', 'level': 2, 'score': 0.79172}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.64546895}, {'id': 'https://openalex.org/C121705324', 'wikidata': 'https://www.wikidata.org/wiki/Q1510587', 'display_name': 'Pseudo-Riemannian manifold', 'level': 4, 'score': 0.6103369}, {'id': 'https://openalex.org/C529865628', 'wikidata': 'https://www.wikidata.org/wiki/Q1790740', 'display_name': 'Manifold (fluid mechanics)', 'level': 2, 'score': 0.59513485}, {'id': 'https://openalex.org/C571446', 'wikidata': 'https://www.wikidata.org/wiki/Q6510183', 'display_name': 'Diffusion equation', 'level': 3, 'score': 0.5301232}, {'id': 'https://openalex.org/C70615421', 'wikidata': 'https://www.wikidata.org/wiki/Q339444', 'display_name': "Laplace's equation", 'level': 3, 'score': 0.5240598}, {'id': 'https://openalex.org/C2778572836', 'wikidata': 'https://www.wikidata.org/wiki/Q380933', 'display_name': 'Space (punctuation)', 'level': 2, 'score': 0.4833045}, {'id': 'https://openalex.org/C154249771', 'wikidata': 'https://www.wikidata.org/wiki/Q1339058', 'display_name': 'Fractional calculus', 'level': 2, 'score': 0.47353145}, {'id': 'https://openalex.org/C62354387', 'wikidata': 'https://www.wikidata.org/wiki/Q875399', 'display_name': 'Boundary (topology)', 'level': 2, 'score': 0.46935377}, {'id': 'https://openalex.org/C12089564', 'wikidata': 'https://www.wikidata.org/wiki/Q1195879', 'display_name': 'Ricci curvature', 'level': 3, 'score': 0.3810916}, {'id': 'https://openalex.org/C182310444', 'wikidata': 'https://www.wikidata.org/wiki/Q1332643', 'display_name': 'Boundary value problem', 'level': 2, 'score': 0.256043}, {'id': 'https://openalex.org/C176217482', 'wikidata': 'https://www.wikidata.org/wiki/Q860554', 'display_name': 'Metric (unit)', 'level': 2, 'score': 0.100177675}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.08484855}, {'id': 'https://openalex.org/C41895202', 'wikidata': 'https://www.wikidata.org/wiki/Q8162', 'display_name': 'Linguistics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C78519656', 'wikidata': 'https://www.wikidata.org/wiki/Q101333', 'display_name': 'Mechanical engineering', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C21547014', 'wikidata': 'https://www.wikidata.org/wiki/Q1423657', 'display_name': 'Operations management', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C195065555', 'wikidata': 'https://www.wikidata.org/wiki/Q214881', 'display_name': 'Curvature', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1016/j.jde.2020.05.022', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S200871675', 'display_name': 'Journal of Differential Equations', 'issn_l': '0022-0396', 'issn': ['0022-0396', '1090-2732'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1903.04348', 'pdf_url': 'https://arxiv.org/pdf/1903.04348', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1903.04348', 'pdf_url': 'https://arxiv.org/pdf/1903.04348', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [{'funder': 'https://openalex.org/F4320310086', 'funder_display_name': 'Helsingin Yliopisto', 'award_id': None}, {'funder': 'https://openalex.org/F4320321108', 'funder_display_name': 'Academy of Finland', 'award_id': '284715'}, {'funder': 'https://openalex.org/F4320321108', 'funder_display_name': 'Academy of Finland', 'award_id': '273979'}, {'funder': 'https://openalex.org/F4320321108', 'funder_display_name': 'Academy of Finland', 'award_id': '312110'}, {'funder': 'https://openalex.org/F4320321108', 'funder_display_name': 'Academy of Finland', 'award_id': '314879'}], 'datasets': [], 'versions': [], 'referenced_works_count': 80, 'referenced_works': ['https://openalex.org/W1507925093', 'https://openalex.org/W1530054495', 'https://openalex.org/W1531503646', 'https://openalex.org/W1584611818', 'https://openalex.org/W1597209545', 'https://openalex.org/W1602064551', 'https://openalex.org/W1855169650', 'https://openalex.org/W1972478479', 'https://openalex.org/W1983959946', 'https://openalex.org/W1985839840', 'https://openalex.org/W1991866677', 'https://openalex.org/W1998214447', 'https://openalex.org/W2018008937', 'https://openalex.org/W2022084521', 'https://openalex.org/W2022685032', 'https://openalex.org/W2028065029', 'https://openalex.org/W2030749893', 'https://openalex.org/W2030765885', 'https://openalex.org/W2034839545', 'https://openalex.org/W2034865749', 'https://openalex.org/W2041540906', 'https://openalex.org/W2043922553', 'https://openalex.org/W2046740511', 'https://openalex.org/W2047833390', 'https://openalex.org/W2054386976', 'https://openalex.org/W2055701161', 'https://openalex.org/W2059742207', 'https://openalex.org/W2060240831', 'https://openalex.org/W2062094097', 'https://openalex.org/W2063887534', 'https://openalex.org/W2066060749', 'https://openalex.org/W2066686577', 'https://openalex.org/W2079961897', 'https://openalex.org/W2092525487', 'https://openalex.org/W2092912961', 'https://openalex.org/W2108283493', 'https://openalex.org/W2119671522', 'https://openalex.org/W2151015649', 'https://openalex.org/W2157452532', 'https://openalex.org/W2158112438', 'https://openalex.org/W2259227674', 'https://openalex.org/W2490499640', 'https://openalex.org/W2529709434', 'https://openalex.org/W2582639083', 'https://openalex.org/W2610195475', 'https://openalex.org/W2619423951', 'https://openalex.org/W2732661672', 'https://openalex.org/W2739814087', 'https://openalex.org/W2742159529', 'https://openalex.org/W2753231176', 'https://openalex.org/W2782599461', 'https://openalex.org/W2783811661', 'https://openalex.org/W2789921513', 'https://openalex.org/W2884870038', 'https://openalex.org/W2891093296', 'https://openalex.org/W2891620995', 'https://openalex.org/W2894725176', 'https://openalex.org/W2894947447', 'https://openalex.org/W2954557599', 'https://openalex.org/W2962999590', 'https://openalex.org/W2963167431', 'https://openalex.org/W2963355286', 'https://openalex.org/W2964325924', 'https://openalex.org/W3021722416', 'https://openalex.org/W3038830718', 'https://openalex.org/W3098690120', 'https://openalex.org/W3099393693', 'https://openalex.org/W3100087909', 'https://openalex.org/W3100191454', 'https://openalex.org/W3100302985', 'https://openalex.org/W3101029882', 'https://openalex.org/W3106219215', 'https://openalex.org/W3106392827', 'https://openalex.org/W3106488876', 'https://openalex.org/W3125755367', 'https://openalex.org/W4214757991', 'https://openalex.org/W4293200410', 'https://openalex.org/W4312224081', 'https://openalex.org/W605875166', 'https://openalex.org/W617317968'], 'related_works': ['https://openalex.org/W75295478', 'https://openalex.org/W4362679437', 'https://openalex.org/W3035440551', 'https://openalex.org/W2962697612', 'https://openalex.org/W2921922410', 'https://openalex.org/W2756320385', 'https://openalex.org/W2368958746', 'https://openalex.org/W2188567613', 'https://openalex.org/W2106710765', 'https://openalex.org/W111226532'], 'abstract_inverted_index': {'Given': [0], 'a': [1, 12, 85, 104], 'connected': [2], 'compact': [3], 'Riemannian': [4, 105], 'manifold': [5, 101], '(M,g)': [6], 'without': [7], 'boundary,': [8], 'dim\u2061M≥2,': [9], 'we': [10], 'consider': [11], 'space–time': [13], 'fractional': [14, 50], 'diffusion': [15], 'equation': [16, 37, 74], 'with': [17], 'an': [18, 25, 79], 'interior': [19], 'source': [20, 87], 'that': [21, 89], 'is': [22, 38, 58, 78], 'supported': [23], 'on': [24, 62, 75, 97], 'open': [26], 'subset': [27], 'V': [28, 98], 'of': [29, 35, 44, 93], 'the': [30, 36, 41, 48, 59, 63, 71, 76, 91, 94, 100], 'manifold.': [31, 64], 'The': [32, 65], 'time-fractional': [33], 'part': [34, 51], 'given': [39], 'by': [40, 52], 'Caputo': [42], 'derivative': [43], 'order': [45], 'α∈(0,1],': [46], 'and': [47, 56], 'space': [49], '(−Δg)β,': [53], 'where': [54], 'β∈(0,1]': [55], 'Δg': [57], 'Laplace–Beltrami': [60], 'operator': [61], 'case': [66], 'α=β=1,': [67], 'which': [68], 'corresponds': [69], 'to': [70, 103], 'standard': [72], 'heat': [73], 'manifold,': [77], 'important': [80], 'special': [81], 'case.': [82], 'We': [83], 'construct': [84], 'specific': [86], 'such': [88], 'measuring': [90], 'evolution': [92], 'corresponding': [95], 'solution': [96], 'determines': [99], 'up': [102], 'isometry.': [106]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3035440551', 'counts_by_year': [{'year': 2024, 'cited_by_count': 4}, {'year': 2023, 'cited_by_count': 4}, {'year': 2022, 'cited_by_count': 3}, {'year': 2021, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 4}], 'updated_date': '2024-09-19T23:59:09.618361', 'created_date': '2020-06-19'}