{"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
We investigate the relation between the level set approach and the varifold approach for the mean curvature flow with Neumann boundary conditions. With an appropriate initial data, we prove that the almost all level sets of the unique viscosity level set solution satisfy Brakke's inequality and a generalized Neumann boundary condition.
{"title":"Level set mean curvature flow, with Neumann boundary conditions","authors":"Satoru Aimi","doi":"10.14492/hokmj/2020-426","DOIUrl":"https://doi.org/10.14492/hokmj/2020-426","url":null,"abstract":"We investigate the relation between the level set approach and the varifold approach for the mean curvature flow with Neumann boundary conditions. With an appropriate initial data, we prove that the almost all level sets of the unique viscosity level set solution satisfy Brakke's inequality and a generalized Neumann boundary condition.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44525976","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 present a precise discussion of Golubitsky and Schaeffer's treatment on bifurcation of Euler buckling problem. We discuss smoothness of the problem and derive equations describing the bifurcation set $B$ and the hysteresis set $H$ up to order 3, which enable us to draw their figures approximately under suitable assumptions.
{"title":"Bifurcation of Euler buckling problem, revisited","authors":"Atia Afroz, Toshizumi Fukui","doi":"10.14492/hokmj/2018-910","DOIUrl":"https://doi.org/10.14492/hokmj/2018-910","url":null,"abstract":"We present a precise discussion of Golubitsky and Schaeffer's treatment on bifurcation of Euler buckling problem. We discuss smoothness of the problem and derive equations describing the bifurcation set $B$ and the hysteresis set $H$ up to order 3, which enable us to draw their figures approximately under suitable assumptions.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49002750","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 fourth order nonlinear Schrodinger equation begin{equation*} i{partial }_{t}u-frac{1}{4}partial _{x}^{4}u=f(u) ,quad (t,x)in mathbb{R}times mathbb{R}, end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.
{"title":"Scattering operator for the fourth order nonlinear Schrüdinger equation","authors":"N. Hayashi, Yuichiro Kawahara, P. Naumkin","doi":"10.14492/hokmj/2018-907","DOIUrl":"https://doi.org/10.14492/hokmj/2018-907","url":null,"abstract":"We study the fourth order nonlinear Schrodinger equation begin{equation*} i{partial }_{t}u-frac{1}{4}partial _{x}^{4}u=f(u) ,quad (t,x)in mathbb{R}times mathbb{R}, end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44702146","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}
Let $(R,frak{m})$ be a Noetherian local ring, $frak{a}$ an ideal of $R$ and $M$ a finitely generated $R$-module. In this paper, we study Colocalization of formal local cohomology modules. Here, similar to the local global Principle in local cohomology theory, we investigate artinianness and minimaxness of formal local cohomology modules in terms of their colocalizations. Among other things, we will prove that, for any integer $n$, $mathfrak{F}_{frak{a}}^i(M)$ is artinian $R$-module for all $i lt n$, if and only if $_{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)$. Also, $ mathfrak{F}_{frak{a}}^i(M) $ is minimax $R$-module for all $i lt n$, if and only if $ _{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)setminuslbrace frak{m}rbrace$.
{"title":"Colocalization of formal local cohomology modules","authors":"S. Rezaei","doi":"10.14492/hokmj/2018-906","DOIUrl":"https://doi.org/10.14492/hokmj/2018-906","url":null,"abstract":"Let $(R,frak{m})$ be a Noetherian local ring, $frak{a}$ an ideal of $R$ and $M$ a finitely generated $R$-module. In this paper, we study Colocalization of formal local cohomology modules. Here, similar to the local global Principle in local cohomology theory, we investigate artinianness and minimaxness of formal local cohomology modules in terms of their colocalizations. Among other things, we will prove that, for any integer $n$, $mathfrak{F}_{frak{a}}^i(M)$ is artinian $R$-module for all $i lt n$, if and only if $_{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)$. Also, $ mathfrak{F}_{frak{a}}^i(M) $ is minimax $R$-module for all $i lt n$, if and only if $ _{frak{p}}(mathfrak{F}_{frak{a}}^i(M)) $ is representable $R_{frak{p}}$-module for all $i lt n$ and all $frak{p} in operatorname{Spec}(R)setminuslbrace frak{m}rbrace$.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48503351","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936538
M. Shirali, E. Momtahan, S. Safaeeyan
{"title":"Perpendicular graph of modules","authors":"M. Shirali, E. Momtahan, S. Safaeeyan","doi":"10.14492/hokmj/1607936538","DOIUrl":"https://doi.org/10.14492/hokmj/1607936538","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49089918","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}
Pub Date : 2020-10-01DOI: 10.14492/hokmj/1607936536
Masaya Kawamura
{"title":"On Kähler-like almost Hermitian metrics and the almost Hermitian curvature flow","authors":"Masaya Kawamura","doi":"10.14492/hokmj/1607936536","DOIUrl":"https://doi.org/10.14492/hokmj/1607936536","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43183094","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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