Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term
The main goal of this work is to investigate the initial boundary value problem of nonlinear wave equation with weak and strong damping terms and logarithmic term at three different initial energy levels, i.e., subcritical energy (0) < , critical initial energy (0) = and the arbitrary high initia...
Saved in:
| Published in | Advances in nonlinear analysis Vol. 9; no. 1; pp. 613 - 632 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.01.2020
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The main goal of this work is to investigate the initial boundary value problem of nonlinear wave equation with weak and strong damping terms and logarithmic term at three different initial energy levels, i.e., subcritical energy
(0) <
, critical initial energy
(0) =
and the arbitrary high initial energy
(0) > 0 (
= 0). Firstly, we prove the local existence of weak solution by using contraction mapping principle. And in the framework of potential well, we show the global existence, energy decay and, unlike the power type nonlinearity, infinite time blow up of the solution with sub-critical initial energy. Then we parallelly extend all the conclusions for the subcritical case to the critical case by scaling technique. Besides, a high energy infinite time blow up result is established. |
|---|---|
| AbstractList | The main goal of this work is to investigate the initial boundary value problem of nonlinear wave equation with weak and strong damping terms and logarithmic term at three different initial energy levels, i.e., subcritical energy
(0) <
, critical initial energy
(0) =
and the arbitrary high initial energy
(0) > 0 (
= 0). Firstly, we prove the local existence of weak solution by using contraction mapping principle. And in the framework of potential well, we show the global existence, energy decay and, unlike the power type nonlinearity, infinite time blow up of the solution with sub-critical initial energy. Then we parallelly extend all the conclusions for the subcritical case to the critical case by scaling technique. Besides, a high energy infinite time blow up result is established. The main goal of this work is to investigate the initial boundary value problem of nonlinear wave equation with weak and strong damping terms and logarithmic term at three different initial energy levels, i.e., subcritical energy E (0) < d , critical initial energy E (0) = d and the arbitrary high initial energy E (0) > 0 ( ω = 0). Firstly, we prove the local existence of weak solution by using contraction mapping principle. And in the framework of potential well, we show the global existence, energy decay and, unlike the power type nonlinearity, infinite time blow up of the solution with sub-critical initial energy. Then we parallelly extend all the conclusions for the subcritical case to the critical case by scaling technique. Besides, a high energy infinite time blow up result is established. The main goal of this work is to investigate the initial boundary value problem of nonlinear wave equation with weak and strong damping terms and logarithmic term at three different initial energy levels, i.e., subcritical energy E(0) < d, critical initial energy E(0) = d and the arbitrary high initial energy E(0) > 0 (ω = 0). Firstly, we prove the local existence of weak solution by using contraction mapping principle. And in the framework of potential well, we show the global existence, energy decay and, unlike the power type nonlinearity, infinite time blow up of the solution with sub-critical initial energy. Then we parallelly extend all the conclusions for the subcritical case to the critical case by scaling technique. Besides, a high energy infinite time blow up result is established. |
| Author | Lian, Wei Xu, Runzhang |
| Author_xml | – sequence: 1 givenname: Wei surname: Lian fullname: Lian, Wei organization: College of Automation, Harbin Engineering University, Harbin, People’s Republic of China – sequence: 2 givenname: Runzhang surname: Xu fullname: Xu, Runzhang organization: College of Mathematical Sciences, Harbin Engineering University, Harbin, People’s Republic of China |
| BookMark | eNp9kEFLJDEQhcOisOrOea_5A61Jp9PpgBcRdQcGvCjsLVSnq8fMZjpj0uPgvzfTs4gIGgJVyav3oL5TcjSEAQn5zdk5l1xeQH5DUbKSFYzx-gc5KbnmhZbs79GH_ieZpbRi-TSSK8VOSLjzoQVPd-h9sQkJuwFToqGnOdG7ASHSHbwgxectjC4MdOfGpzwO_ygMHU1jDMOSdrDeuFxHjOs0CT4sIebRtbM0hW20OIm_yHEPPuHsfz0jj7c3D9d_isX93fz6alHYivGxaMHWlUSUssayZbUSKBrbKpCt0L2wdd_WspFYamgq2VQi62hVXp0pi0yJMzI_5HYBVmYT3RriqwngzPQR4tJAHJ31aATWva50BRpzlug1K7v9rRS3lqs-Z10csmwMKUXs3_M4M3v8ZsJv9vjNHn92yE8O68YJ3xjB-W98lwffDnym1eEybl9zY1aZ4JB5feXUvOZCvAGNQKI7 |
| CitedBy_id | crossref_primary_10_1111_sapm_12405 crossref_primary_10_3934_math_20221006 crossref_primary_10_3934_dcdss_2021122 crossref_primary_10_1007_s13226_023_00518_8 crossref_primary_10_3934_dcdss_2021125 crossref_primary_10_1016_j_padiff_2024_100984 crossref_primary_10_3934_mbe_2023225 crossref_primary_10_1016_j_jde_2021_10_036 crossref_primary_10_3934_era_2020034 crossref_primary_10_1007_s12220_024_01747_x crossref_primary_10_1007_s12215_021_00698_4 crossref_primary_10_3934_dcdss_2021110 crossref_primary_10_1515_anly_2023_0072 crossref_primary_10_1016_j_na_2019_111729 crossref_primary_10_3934_dcdss_2021112 crossref_primary_10_1111_sapm_12498 crossref_primary_10_3934_math_20241425 crossref_primary_10_1016_j_jmaa_2022_126132 crossref_primary_10_3934_dcdss_2021114 crossref_primary_10_3934_dcdss_2021115 crossref_primary_10_1186_s13661_022_01634_w crossref_primary_10_3390_axioms13100709 crossref_primary_10_3934_dcdss_2021108 crossref_primary_10_3934_era_2020021 crossref_primary_10_3934_era_2020020 crossref_primary_10_3934_math_2023046 crossref_primary_10_3390_mca27010010 crossref_primary_10_3934_era_2021073 crossref_primary_10_12677_AAM_2023_124152 crossref_primary_10_3934_era_2020025 crossref_primary_10_1007_s42985_022_00207_x crossref_primary_10_3934_cam_2023012 crossref_primary_10_1016_j_na_2020_111832 crossref_primary_10_1002_mana_202000266 crossref_primary_10_1080_00036811_2022_2125387 crossref_primary_10_1186_s13661_020_01374_9 crossref_primary_10_3934_mbe_2023174 crossref_primary_10_1140_epjp_s13360_020_00568_5 crossref_primary_10_11650_tjm_220702 crossref_primary_10_1186_s13661_021_01535_4 crossref_primary_10_1002_mma_8912 crossref_primary_10_1515_anona_2021_0207 crossref_primary_10_1515_anona_2022_0267 crossref_primary_10_1515_anona_2023_0115 crossref_primary_10_3934_cam_2023021 crossref_primary_10_1007_s00245_020_09704_0 crossref_primary_10_1016_j_aml_2023_108954 crossref_primary_10_1002_mana_202300275 crossref_primary_10_1186_s13661_022_01611_3 crossref_primary_10_1016_j_nonrwa_2023_103958 crossref_primary_10_3233_ASY_201621 crossref_primary_10_1016_j_apnum_2020_06_002 crossref_primary_10_3934_math_2024627 crossref_primary_10_1186_s13661_020_01382_9 crossref_primary_10_1002_mma_9684 crossref_primary_10_1186_s13661_020_01357_w crossref_primary_10_3934_math_20231404 crossref_primary_10_1002_mma_7812 crossref_primary_10_1155_2022_9801331 crossref_primary_10_1016_j_jmaa_2024_128408 crossref_primary_10_1080_00036811_2023_2241493 crossref_primary_10_3934_era_2024248 crossref_primary_10_1515_ans_2022_0024 crossref_primary_10_1016_j_na_2020_111898 crossref_primary_10_1186_s13661_020_01438_w crossref_primary_10_1186_s13662_020_02694_x crossref_primary_10_1016_j_na_2020_111776 crossref_primary_10_1186_s13662_020_03037_6 crossref_primary_10_3934_math_2021326 crossref_primary_10_1515_anona_2024_0015 crossref_primary_10_3390_fractalfract6100581 crossref_primary_10_1002_zamm_202000094 crossref_primary_10_3934_math_20231018 crossref_primary_10_1186_s13661_019_01308_0 crossref_primary_10_1007_s00009_023_02469_0 crossref_primary_10_1186_s13661_020_01482_6 crossref_primary_10_1186_s13661_019_1266_1 crossref_primary_10_1016_j_na_2020_111885 crossref_primary_10_3934_cam_2023008 crossref_primary_10_1002_mma_10343 crossref_primary_10_1002_mma_10100 crossref_primary_10_1112_jlms_70091 crossref_primary_10_1016_j_apnum_2022_08_014 crossref_primary_10_1016_j_nonrwa_2024_104209 crossref_primary_10_1016_j_cnsns_2024_108450 crossref_primary_10_1063_5_0149240 crossref_primary_10_1016_j_apnum_2022_12_017 crossref_primary_10_3390_math13020319 crossref_primary_10_1016_j_na_2020_111752 crossref_primary_10_1016_j_na_2020_111873 crossref_primary_10_3934_era_2020019 crossref_primary_10_1016_j_na_2020_111759 crossref_primary_10_36753_mathenot_1084371 crossref_primary_10_3934_math_2021425 crossref_primary_10_1007_s13324_025_01017_1 crossref_primary_10_1016_j_aml_2024_109290 crossref_primary_10_1007_s00033_023_02177_5 crossref_primary_10_1002_mma_9007 crossref_primary_10_3934_era_2021066 crossref_primary_10_1080_00036811_2023_2253830 crossref_primary_10_3934_mbe_2022398 crossref_primary_10_1155_2021_9924504 crossref_primary_10_11650_tjm_220107 crossref_primary_10_3934_era_2020016 crossref_primary_10_3934_era_2020015 crossref_primary_10_1134_S0965542523060192 crossref_primary_10_3233_ASY_211731 crossref_primary_10_1016_j_nonrwa_2022_103587 crossref_primary_10_1016_j_apnum_2023_01_010 crossref_primary_10_1007_s13324_023_00782_1 crossref_primary_10_1016_j_na_2020_111866 crossref_primary_10_1016_j_na_2020_111864 crossref_primary_10_3934_dcdss_2021134 crossref_primary_10_3934_dcdss_2021135 crossref_primary_10_1186_s13661_022_01633_x crossref_primary_10_1016_j_na_2019_111664 crossref_primary_10_3934_era_2021052 crossref_primary_10_3934_era_2020006 crossref_primary_10_3934_cam_2025011 crossref_primary_10_3934_era_2020088 crossref_primary_10_1007_s10883_020_09522_1 crossref_primary_10_3934_era_2020003 crossref_primary_10_3934_era_2020002 crossref_primary_10_3934_era_2021057 |
| Cites_doi | 10.1006/jdeq.1998.3477 10.1007/BF00250942 10.1143/PTPS.190.229 10.1007/BF02761595 10.4208/jpde.v28.n3.5 10.1090/gsm/014 10.2307/2373688 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.1515/anona-2020-0016 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 2191-950X |
| EndPage | 632 |
| ExternalDocumentID | oai_doaj_org_article_3e6f9494a9e8453f902d02d0471cc17f 10_1515_anona_2020_0016 10_1515_anona_2020_001691613 |
| GroupedDBID | 0R~ 0~D 4.4 AAFPC AAFWJ AAQCX AASOL AASQH AAWFC ABAOT ABAQN ABFKT ABIQR ABSOE ABUVI ABXMZ ACGFS ACMKP ACXLN ACZBO ADGQD ADGYE ADJVZ ADOZN AEJTT AEKEB AENEX AEQDQ AEXIE AFBAA AFBDD AFCXV AFPKN AFQUK AHGSO AIERV AIKXB AJATJ AKXKS ALMA_UNASSIGNED_HOLDINGS AMVHM BAKPI BBCWN CFGNV EBS GROUPED_DOAJ HZ~ IY9 J9A M48 O9- OK1 QD8 SA. SLJYH AAYXX CITATION |
| ID | FETCH-LOGICAL-c401t-bac645ee556e2b0673e38cb7a5b39f3c6fb6585e29a8458433e3ec701607ce073 |
| IEDL.DBID | DOA |
| ISSN | 2191-950X |
| IngestDate | Wed Aug 27 01:06:31 EDT 2025 Thu Apr 24 22:55:18 EDT 2025 Tue Jul 01 00:37:48 EDT 2025 Thu Jul 10 10:37:34 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| License | This work is licensed under the Creative Commons Attribution 4.0 Public License. http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c401t-bac645ee556e2b0673e38cb7a5b39f3c6fb6585e29a8458433e3ec701607ce073 |
| OpenAccessLink | https://doaj.org/article/3e6f9494a9e8453f902d02d0471cc17f |
| PageCount | 20 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_3e6f9494a9e8453f902d02d0471cc17f crossref_primary_10_1515_anona_2020_0016 crossref_citationtrail_10_1515_anona_2020_0016 walterdegruyter_journals_10_1515_anona_2020_001691613 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2020-01-01 |
| PublicationDateYYYYMMDD | 2020-01-01 |
| PublicationDate_xml | – month: 01 year: 2020 text: 2020-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Advances in nonlinear analysis |
| PublicationYear | 2020 |
| Publisher | De Gruyter |
| Publisher_xml | – name: De Gruyter |
| References | 2021020917371768664_j_anona-2020-0016_ref_005 2021020917371768664_j_anona-2020-0016_ref_016 2021020917371768664_j_anona-2020-0016_ref_006 2021020917371768664_j_anona-2020-0016_ref_017 2021020917371768664_j_anona-2020-0016_ref_003 2021020917371768664_j_anona-2020-0016_ref_014 2021020917371768664_j_anona-2020-0016_ref_004 2021020917371768664_j_anona-2020-0016_ref_015 2021020917371768664_j_anona-2020-0016_ref_001 2021020917371768664_j_anona-2020-0016_ref_012 2021020917371768664_j_anona-2020-0016_ref_002 2021020917371768664_j_anona-2020-0016_ref_013 2021020917371768664_j_anona-2020-0016_ref_010 2021020917371768664_j_anona-2020-0016_ref_011 2021020917371768664_j_anona-2020-0016_ref_020 2021020917371768664_j_anona-2020-0016_ref_009 2021020917371768664_j_anona-2020-0016_ref_007 2021020917371768664_j_anona-2020-0016_ref_018 2021020917371768664_j_anona-2020-0016_ref_008 2021020917371768664_j_anona-2020-0016_ref_019 |
| References_xml | – ident: 2021020917371768664_j_anona-2020-0016_ref_012 – ident: 2021020917371768664_j_anona-2020-0016_ref_009 – ident: 2021020917371768664_j_anona-2020-0016_ref_008 – ident: 2021020917371768664_j_anona-2020-0016_ref_007 – ident: 2021020917371768664_j_anona-2020-0016_ref_015 – ident: 2021020917371768664_j_anona-2020-0016_ref_013 – ident: 2021020917371768664_j_anona-2020-0016_ref_010 – ident: 2021020917371768664_j_anona-2020-0016_ref_011 – ident: 2021020917371768664_j_anona-2020-0016_ref_017 – ident: 2021020917371768664_j_anona-2020-0016_ref_018 – ident: 2021020917371768664_j_anona-2020-0016_ref_005 doi: 10.1006/jdeq.1998.3477 – ident: 2021020917371768664_j_anona-2020-0016_ref_001 – ident: 2021020917371768664_j_anona-2020-0016_ref_004 – ident: 2021020917371768664_j_anona-2020-0016_ref_002 doi: 10.1007/BF00250942 – ident: 2021020917371768664_j_anona-2020-0016_ref_014 doi: 10.1143/PTPS.190.229 – ident: 2021020917371768664_j_anona-2020-0016_ref_006 – ident: 2021020917371768664_j_anona-2020-0016_ref_003 doi: 10.1007/BF02761595 – ident: 2021020917371768664_j_anona-2020-0016_ref_016 doi: 10.4208/jpde.v28.n3.5 – ident: 2021020917371768664_j_anona-2020-0016_ref_020 doi: 10.1090/gsm/014 – ident: 2021020917371768664_j_anona-2020-0016_ref_019 doi: 10.2307/2373688 |
| SSID | ssj0000851770 |
| Score | 2.5216367 |
| Snippet | The main goal of this work is to investigate the initial boundary value problem of nonlinear wave equation with weak and strong damping terms and logarithmic... |
| SourceID | doaj crossref walterdegruyter |
| SourceType | Open Website Enrichment Source Index Database Publisher |
| StartPage | 613 |
| SubjectTerms | energy decay global solution infinite time blow up logarithmic nonlinearity Wave equation weak and strong damping terms |
| SummonAdditionalLinks | – databaseName: Scholars Portal Journals: Open Access dbid: M48 link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9wwELZaeikHBH2ILQ_5wIFLtmT9SHxACBAIIdETK-0tsp3xFtgX2VDg3zPjZGlBcKuUU2zL9ow9L9vfMLZTklbwkCcqMyaRoG1iHAXyS5tbIYxOA4UGLn7ps748H6jB33RALQHnb7p2lE-qX426D7ePB7jh92P2nlT9tOgoW2R3j95Ip_oj-4QDyGiXXrS2_nVzISvNsr0W3ueNdi80UwTwX2Yr9_HQuoRhdfdYLw5Jo-45XWUrrdHIDxsur7EPMPnClv-BEvzKpg14P6dYXDKbzqEkGcangU8aMAxb8Xv7BzjcNuDenCKwWN3ecDsp-ZxC4kNe2jE9oOIksOexAGUjutP17_GV502kPxZ-Y_3Tk8vjs6RNppB4dKHqxFmvpQJQSkPPUXoaELl3mVVOmCC8Dg6NEQU9Y3M6OxVYDj6LAHQeUBB8Z0s4YFhnHC3C3KMnUsrgZGa9C2CU9J4e5aYilx3WXRCy8C3SOCW8GBXkcSDli0j5gihPd-p0h-0-N5g1IBvvVz0izjxXI3Ts-GNaDYt2sxUCdDDSSGsA5yKC2euV9KEi9j7NQoepV3wtFgvvvX7Rik7Fj__R-Qb73Cw5CuNssqW6uoMtNGxqtx0X7BOUfPhe priority: 102 providerName: Scholars Portal |
| Title | Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term |
| URI | https://www.degruyter.com/doi/10.1515/anona-2020-0016 https://doaj.org/article/3e6f9494a9e8453f902d02d0471cc17f |
| Volume | 9 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA6yJz2IT1xf5ODBS9VukrY5qiiLoCcX9laSdOJzH-52Ff-9M0ldFkG8CKWHTkrCZDKvJN8wdlSRVXBQJCrXOpGQmURbSuRXpjBC6Cz1lBq4vcu6PXnTV_2FUl90JizCA0fGnQrIvJZaGg2FVMLrs05FDypV59Lck_ZFm7cQTD3H01dpnp81WD5os08NRtMGZaJDF6mpuvmCGQpo_Sts9SPsUFfwMJl91t87osHQXK-x1cZD5OdxZOtsCYYbbGUBN3CTjSJSP6fEWzIeTaEihcVHng8j8oWZ8A_zDhzeIpI3p3QrNjcv3AwrPqX89wOvzIBuS3HSztNAQEWIsXP9OHhyPKb1A3GL9a6v7i-7SVM5IXEYL9WJNS6TCkCpDDqWatGAKJzNjbJCe-Eyb9HzUNDRpqCNUoF0cHlAm3OAq36btXDAsMM4un-Fw7Cjkt7K3DjrQSvpHN3ATUUh2-zkm5Gla2DFqbrFa0nhBXK-DJwvifN0gC5rs-P5D-OIqPF70wuamXkzgsIOH1BAykZAyr8EpM3Uj3ktm2U6_a1fdJlTsfsfne-x5ShylLPZZ616MoMD9GJqexgEFt-3svgCqXPxHg |
| linkProvider | Directory of Open Access Journals |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB7R5dByQPSlbh_Uhx56SZesH4mPFBW2LdBDQeIWOfZ4QWU3dDdb1H_fmSREtIJLpZxiW3FmbM_MZ89ngHeBrYLHPNGZtYlC4xJbMpAfXO6ktCaNDA0cHZvJqfpyps_WYO8mF4aPVQacLla_65YhdRQqv2KgrOcaIAs8chQbO9LwmNOiUzM6r2eXD2DdkPufD2B9d3Lw_VsPtbBXkWU7HbHPHc3_skkNdf8GbF4329V9X25Znf0t2OzcRbHb6vcxrOH8CWzcIhF8ClVL2y8YhUuuqiUGXr1EFcW8pcFwC3HtfqHAny2tt2Dslaq7H8LNg1gyGD4Vwc04dUrwUr1sCmhVpEC6Pp9deNFi_E3hMzjd_3SyN0m6axQST8FTnZTOG6URtTY4LvliGpS5LzOnS2mj9CaW5IZoHFuX866ppHL0WUM955GWgOcwoA7jCxDkC-aeYpCgYqky58uIVivvOR03lbkawocbQRa-4xjnqy4uC441SPJFI_mCJc-n6cwQ3vcNrlp6jfurfmTN9NWYF7t5US2mRTfNCokmWmWVs0j_IqPdGQd-yAR7n2ZxCPofvRbdnF3e913yn1P58j_bvYWHk5Ojw-Lw8_HXV_CoHXGM37yGQb1Y4RvyaOpyuxuxfwDSrvTf |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwEB7BVkL0UPFUl0LxgQOXsM3aceJjgS7LqyBBpd4iP8YLgm6W3Wyr_ntmkjRaEL0g5RTbijNje2Y-ez4DPAtsFTwWSZYbkyjUNjGOgfxgCyul0WlkaODjsZ6eqHen2elGLgwfqww4W64v65YhdRQqv2agrOcaIAs8shQbW9LwmNOiUz1ahHgTtrQ2Ug1g63D65sunHmlhpyLPDzpen3-0_sMkNcz927Bz0exW913ZMDqTO7DTeYvisFXvXbiB83uwvcEheB-qlrVfMAiXLKoVBl68RBXFvGXBsEtxYc9R4K-W1Vsw9ErV7Q9h50GsGAufiWDPOHNK8Eq9agpoUaQ4uv529t2LFuJvCh_AyeTo66tp0t2ikHiKnerEWa9VhphlGseO76VBWXiX28xJE6XX0ZEXkuHY2II3TSWVo88b5jmPtAI8hAF1GHdBkCtYeApBgopO5da7iCZT3nM2bioLNYQXV4IsfUcxzjdd_Cw51CDJl43kS5Y8H6bTQ3jeN1i07BrXV33JmumrMS1286JazspulpUSdTTKKGuQ_kVGczAO_JAF9j7N4xCyv_RadlN2dd13yX1O5aP_bPcUbn1-PSk_vD1-vwe32wHH6M1jGNTLNT4hf6Z2-92A_Q1aMfQF |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Global+well-posedness+of+nonlinear+wave+equation+with+weak+and+strong+damping+terms+and+logarithmic+source+term&rft.jtitle=Advances+in+nonlinear+analysis&rft.au=Lian+Wei&rft.au=Xu+Runzhang&rft.date=2020-01-01&rft.pub=De+Gruyter&rft.eissn=2191-950X&rft.volume=9&rft.issue=1&rft.spage=613&rft.epage=632&rft_id=info:doi/10.1515%2Fanona-2020-0016&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_3e6f9494a9e8453f902d02d0471cc17f |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2191-950X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2191-950X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2191-950X&client=summon |