Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n3.a3
B. Temple, R. Young
{"title":"Inversion of a non-uniform difference operator and a strategy for Nash–Moser","authors":"B. Temple, R. Young","doi":"10.4310/maa.2022.v29.n3.a3","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n3.a3","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70490054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-19DOI: 10.4310/maa.2023.v30.n1.a3
Xiangsheng Xu
In this paper we study a system of partial differential equations which models lithium-ion batteries. The system describes the conservation of Lithium and conservation of charges in the solid and electrolyte phases, together with the conservation of energy. The mathematical challenge is due to the fact that the reaction terms in the system involve the hyperbolic sine function along with possible degeneracy in one of the high order terms. We obtain a local existence assertion for the initial boundary problem for the system which offers insight into how long a battery can last.
{"title":"Life span of solutions to a PDE model for lithium-ion batteries in high space dimensions","authors":"Xiangsheng Xu","doi":"10.4310/maa.2023.v30.n1.a3","DOIUrl":"https://doi.org/10.4310/maa.2023.v30.n1.a3","url":null,"abstract":"In this paper we study a system of partial differential equations which models lithium-ion batteries. The system describes the conservation of Lithium and conservation of charges in the solid and electrolyte phases, together with the conservation of energy. The mathematical challenge is due to the fact that the reaction terms in the system involve the hyperbolic sine function along with possible degeneracy in one of the high order terms. We obtain a local existence assertion for the initial boundary problem for the system which offers insight into how long a battery can last.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43429009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-09DOI: 10.4310/maa.2021.v28.n3.a6
F. Huang, Qian Yuan
Abstract. The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution timeasymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain RˆTn ́1pn ě 2q, where Tn ́1 is the n ́ 1-dimensional torus.
{"title":"Stability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations","authors":"F. Huang, Qian Yuan","doi":"10.4310/maa.2021.v28.n3.a6","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n3.a6","url":null,"abstract":"Abstract. The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution timeasymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain RˆTn ́1pn ě 2q, where Tn ́1 is the n ́ 1-dimensional torus.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48378841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n2.a4
Hua Chen, Jing Wang, Huiyang Xu
{"title":"Global existence, exponential decay and finite time blow-up for a class of finitely degenerate coupled parabolic systems","authors":"Hua Chen, Jing Wang, Huiyang Xu","doi":"10.4310/maa.2021.v28.n2.a4","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n2.a4","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n2.a1
P. Antonelli, P. Marcati, Hao Zheng
{"title":"Dispersive estimates for the QHD system and Euler–Korteweg equations","authors":"P. Antonelli, P. Marcati, Hao Zheng","doi":"10.4310/maa.2021.v28.n2.a1","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n2.a1","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n3.a3
Itsuko Hashimoto, A. Matsumura
{"title":"Existence of radially symmetric stationary solutions for the compressible Navier–Stokes equation","authors":"Itsuko Hashimoto, A. Matsumura","doi":"10.4310/maa.2021.v28.n3.a3","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n3.a3","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n4.a4
C. Miao, Jianwei Yang
{"title":"Oscillatory integrals involving the Carleson–Sjölin conditions and several applications","authors":"C. Miao, Jianwei Yang","doi":"10.4310/maa.2021.v28.n4.a4","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n4.a4","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n3.a5
Rui Huang, Yan-Lv Ren, Jingxue Yin
{"title":"On the existence and monotonicity of curved fronts in a periodic shear flow","authors":"Rui Huang, Yan-Lv Ren, Jingxue Yin","doi":"10.4310/maa.2021.v28.n3.a5","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n3.a5","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n1.a6
Jiaxiang Wang, Bin Zhou
{"title":"Monotonicity formulae for the complex Hessian equations","authors":"Jiaxiang Wang, Bin Zhou","doi":"10.4310/maa.2021.v28.n1.a6","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n1.a6","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/maa.2021.v28.n3.a9
Song Jiang, Q. Ju, Xin Xu
{"title":"Convergence rates of the singular limit for equatorial shallow-water dynamics","authors":"Song Jiang, Q. Ju, Xin Xu","doi":"10.4310/maa.2021.v28.n3.a9","DOIUrl":"https://doi.org/10.4310/maa.2021.v28.n3.a9","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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