{"title":"Global small solutions of the compressible nematic liquid crystal flow in a bounded domain","authors":"Jishan Fan, Jianzhu Sun, T. Tang, G. Nakamura","doi":"10.4064/ap181215-18-5","DOIUrl":"https://doi.org/10.4064/ap181215-18-5","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"124 1","pages":"47-59"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70577991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In [Z. Angew. Math. Phys. 68 (2017)] Apalara considered a one-dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depending on the stability number χτ . In this short note, we continue the study of the same system and show that the solution lacks exponential decay if χτ 6= 0, which solves an open problem proposed by Apalara.
{"title":"Lack of exponential decay for a laminated beam with structural damping and second sound","authors":"Wenjun Liu, Xiangyu Kong, Gang Li","doi":"10.4064/ap181224-17-9","DOIUrl":"https://doi.org/10.4064/ap181224-17-9","url":null,"abstract":"In [Z. Angew. Math. Phys. 68 (2017)] Apalara considered a one-dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depending on the stability number χτ . In this short note, we continue the study of the same system and show that the solution lacks exponential decay if χτ 6= 0, which solves an open problem proposed by Apalara.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"47 11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70578076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the regularity of a semialgebraic function","authors":"A. El-Siblani, K. Kurdyka","doi":"10.4064/ap190719-19-3","DOIUrl":"https://doi.org/10.4064/ap190719-19-3","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"125 1","pages":"25-46"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70579137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A class of maximal plurifinely plurisubharmonic functions in $mathbb C^n$","authors":"Nguyen Thi Lien, H. Can","doi":"10.4064/ap181213-18-5","DOIUrl":"https://doi.org/10.4064/ap181213-18-5","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"124 1","pages":"197-207"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70577943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Theorem of Lion and o-minimal structures which do not admit $mathcal {C}^{infty }$-cell decompositions","authors":"Z. Rożen","doi":"10.4064/ap170626-30-9","DOIUrl":"https://doi.org/10.4064/ap170626-30-9","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"124 1","pages":"291-316"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70573900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. By introducing a new method of estimating the counting function of an auxiliary function, we prove a new general uniqueness theorem for nonarchimedean holomorphic curves sharing few hyperplanes (counted without multiplicities).
{"title":"Generalization of uniqueness theorems for nonarchimedean holomorphic curves","authors":"S. Quang","doi":"10.4064/ap200122-24-4","DOIUrl":"https://doi.org/10.4064/ap200122-24-4","url":null,"abstract":". By introducing a new method of estimating the counting function of an auxiliary function, we prove a new general uniqueness theorem for nonarchimedean holomorphic curves sharing few hyperplanes (counted without multiplicities).","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70580801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability of a suspension bridge with structural damping","authors":"Z. Hajjej, S. Messaoudi","doi":"10.4064/ap191023-4-2","DOIUrl":"https://doi.org/10.4064/ap191023-4-2","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"125 1","pages":"59-70"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70579530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Kirchhoff type problem −m ( Ω w1|∇u| dx ) div(w1|∇u|∇u) = w2f(u) in Ω, u = 0 on ∂Ω, where p ≥ 2, Ω is a C domain of R , w1, w2 are nonnegative functions, m is a positive function and f is an increasing one. Under some assumptions on Ω, w1, w2, m and f , we prove that the problem has no nontrivial stable solution in dimension N < N. Moreover, additional assumptions on Ω, m or the boundedness of solutions can boost this critical dimension N to infinity.
{"title":"Instability of solutions to Kirchhoff type problems in low dimension","authors":"Nhat Vy Huynh, Phuong Le","doi":"10.4064/ap181120-3-5","DOIUrl":"https://doi.org/10.4064/ap181120-3-5","url":null,"abstract":"We study the Kirchhoff type problem −m ( Ω w1|∇u| dx ) div(w1|∇u|∇u) = w2f(u) in Ω, u = 0 on ∂Ω, where p ≥ 2, Ω is a C domain of R , w1, w2 are nonnegative functions, m is a positive function and f is an increasing one. Under some assumptions on Ω, w1, w2, m and f , we prove that the problem has no nontrivial stable solution in dimension N < N. Moreover, additional assumptions on Ω, m or the boundedness of solutions can boost this critical dimension N to infinity.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70577833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Upper bounds on the number of determining nodes for 3D Navier–Stokes–Voigt equations","authors":"V. M. Toi, Nguyễn Thị Ngần","doi":"10.4064/ap190805-19-3","DOIUrl":"https://doi.org/10.4064/ap190805-19-3","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"125 1","pages":"83-99"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70579240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Periodicity and stability of solutions to neutral differential equations with $varphi $-Lipschitz and infinite delays","authors":"Thieu Nguyen, Thi Loan Nguyen, T. N. H. Vu","doi":"10.4064/ap190917-18-5","DOIUrl":"https://doi.org/10.4064/ap190917-18-5","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"125 1","pages":"155-181"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70579406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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