{"title":"Classification of Cartan embeddings which are austere submanifolds","authors":"Taro Kimura, Katsuya Mashimo","doi":"10.14492/hokmj/2019-188","DOIUrl":"https://doi.org/10.14492/hokmj/2019-188","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41852283","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}
The main purpose of the present paper is to study the numerical properties of supersolvable resolutions of line arrangements. We provide upper-bounds on the so-called extension to supersolvability numbers for certain extreme line arrangements in $mathbb{P}^{2}_{mathbb{C}}$ and we show that these numbers textbf{are not} determined by the intersection lattice of the given arrangement.
{"title":"Supersolvable resolutions of line arrangements","authors":"J. Kabat","doi":"10.14492/hokmj/2021-540","DOIUrl":"https://doi.org/10.14492/hokmj/2021-540","url":null,"abstract":"The main purpose of the present paper is to study the numerical properties of supersolvable resolutions of line arrangements. We provide upper-bounds on the so-called extension to supersolvability numbers for certain extreme line arrangements in $mathbb{P}^{2}_{mathbb{C}}$ and we show that these numbers textbf{are not} determined by the intersection lattice of the given arrangement.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48876714","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 Nullstellensatz for ideals of $C^infty$ functions in dimension 2","authors":"Hirofumi Kondo","doi":"10.14492/hokmj/2019-201","DOIUrl":"https://doi.org/10.14492/hokmj/2019-201","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46065346","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":"Blow-up at space infinity for a quasilinear parabolic equation with space-dependent reaction","authors":"Ryuichi Suzuki, Noriaki Umeda","doi":"10.14492/hokmj/2019-195","DOIUrl":"https://doi.org/10.14492/hokmj/2019-195","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47929776","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 this paper, we deal with the chemotaxis-haptotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded convex domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by $L^p$-estimate techniques, we show that the system possesses at least one global and bounded weak solution. Our results generalize and improve previous results.
{"title":"Boundedness of solutions for a quasilinear chemotaxis-haptotaxis model","authors":"Guoqiang Ren, Bing Liu","doi":"10.14492/hokmj/2018-944","DOIUrl":"https://doi.org/10.14492/hokmj/2018-944","url":null,"abstract":"In this paper, we deal with the chemotaxis-haptotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded convex domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by $L^p$-estimate techniques, we show that the system possesses at least one global and bounded weak solution. Our results generalize and improve previous results.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44345114","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 consider the long time behavior of solutions to the initial value problem for the ``complex-valued'' cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the $L^{infty}$ decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).
{"title":"Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension","authors":"J. Segata","doi":"10.14492/hokmj/2018-938","DOIUrl":"https://doi.org/10.14492/hokmj/2018-938","url":null,"abstract":"We consider the long time behavior of solutions to the initial value problem for the ``complex-valued'' cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the $L^{infty}$ decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47766891","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 consider the Riemann problem for fluids of van der Waals type with phase transitions involving nonclassical shocks. The model is elliptic-hyperbolic and the pressure function admits two inflection points. First, a unique classical Riemann solver is constructed, which is based on rarefaction waves, classical shocks and zero-speed shocks. Second, we investigate nonclassical Riemann solvers, which involve nonclassical shocks. Nonclassical shocks are shock waves which violate the Liu entropy condition and satisfy a kinetic relation. It can be shown that then two wave curves always intersect either once or twice at different phases. Consequently, the Riemann problem always admit one or two solutions in the class of classical and nonclassical shocks, zero-speed shocks, and rarefaction waves.
{"title":"The Riemann problem for van der Waals fluids with nonclassical phase transitions","authors":"M. Thanh, Duong Xuan Vinh","doi":"10.14492/hokmj/2019-115","DOIUrl":"https://doi.org/10.14492/hokmj/2019-115","url":null,"abstract":"We consider the Riemann problem for fluids of van der Waals type with phase transitions involving nonclassical shocks. The model is elliptic-hyperbolic and the pressure function admits two inflection points. First, a unique classical Riemann solver is constructed, which is based on rarefaction waves, classical shocks and zero-speed shocks. Second, we investigate nonclassical Riemann solvers, which involve nonclassical shocks. Nonclassical shocks are shock waves which violate the Liu entropy condition and satisfy a kinetic relation. It can be shown that then two wave curves always intersect either once or twice at different phases. Consequently, the Riemann problem always admit one or two solutions in the class of classical and nonclassical shocks, zero-speed shocks, and rarefaction waves.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44767466","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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