{"title":"Stability of polytropic filtration equation with variable exponents","authors":"Huashui Zhan, Zhaosheng Feng","doi":"10.57262/ade/1589594419","DOIUrl":"https://doi.org/10.57262/ade/1589594419","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48805267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Infinitely many solutions for a class of superlinear problems involving variable exponents","authors":"B. Ge, Liyan Wang","doi":"10.57262/ade/1584756039","DOIUrl":"https://doi.org/10.57262/ade/1584756039","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48913440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On ground state of fractional spinor Bose Einstein condensates","authors":"D. Cao, Jinchun He, Haoyuan Xu, Meihua Yang","doi":"10.57262/ade/1584756036","DOIUrl":"https://doi.org/10.57262/ade/1584756036","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49220969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bifurcation of positive radial solutions for a prescribed mean curvature problem on an exterior domain","authors":"Rui Yang, Yong-Hoon Lee","doi":"10.57262/ade/1584756038","DOIUrl":"https://doi.org/10.57262/ade/1584756038","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46469562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-15DOI: 10.57262/ade028-0304-341
Tatsuya Miura
We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong solution to the bulk Navier-Stokes equations converges weakly in appropriate function spaces on the limit surface as the thickness of the thin domain tends to zero. Moreover, we characterize the limit as a weak solution to limit equations, which are the damped and weighted Navier-Stokes equations on the limit surface. We also prove the strong convergence of the average of a strong solution to the bulk equations towards a weak solution to the limit equations by showing estimates for the difference between them. In some special case our limit equations agree with the Navier-Stokes equations on a Riemannian manifold in which the viscous term contains the Ricci curvature. This is the first result on a rigorous derivation of the surface Navier-Stokes equations on a general closed surface by the thin-film limit.
{"title":"Erratum to “Navier–Stokes equations in a curved thin domain, Part III: thin-film limit”","authors":"Tatsuya Miura","doi":"10.57262/ade028-0304-341","DOIUrl":"https://doi.org/10.57262/ade028-0304-341","url":null,"abstract":"We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong solution to the bulk Navier-Stokes equations converges weakly in appropriate function spaces on the limit surface as the thickness of the thin domain tends to zero. Moreover, we characterize the limit as a weak solution to limit equations, which are the damped and weighted Navier-Stokes equations on the limit surface. We also prove the strong convergence of the average of a strong solution to the bulk equations towards a weak solution to the limit equations by showing estimates for the difference between them. In some special case our limit equations agree with the Navier-Stokes equations on a Riemannian manifold in which the viscous term contains the Ricci curvature. This is the first result on a rigorous derivation of the surface Navier-Stokes equations on a general closed surface by the thin-film limit.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44746848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-20DOI: 10.57262/ade026-0910-459
W. Kryszewski, Jakub Siemianowski
We prove the existence of solutions $u$ in $H^1(mathbb{R}^N,mathbb{R}^M)$ of the following strongly coupled semilinear system of second order elliptic PDEs on $mathbb{R}^N$ [ mathcal{P}[u] = f(x,u,nabla u), quad xin mathbb{R}^N, ] whith pointwise constraints. We present the construction of the suitable topoligical degree which allows us to solve the above system on bounded domains. The key step in the proof consists of showing that the sequence of solutions of the truncated system is compact in $H^1$ by the use of the so-called tail estimates.
{"title":"Constrained semilinear elliptic systems on $mathbb R^N$","authors":"W. Kryszewski, Jakub Siemianowski","doi":"10.57262/ade026-0910-459","DOIUrl":"https://doi.org/10.57262/ade026-0910-459","url":null,"abstract":"We prove the existence of solutions $u$ in $H^1(mathbb{R}^N,mathbb{R}^M)$ of the following strongly coupled semilinear system of second order elliptic PDEs on $mathbb{R}^N$ [ mathcal{P}[u] = f(x,u,nabla u), quad xin mathbb{R}^N, ] whith pointwise constraints. We present the construction of the suitable topoligical degree which allows us to solve the above system on bounded domains. The key step in the proof consists of showing that the sequence of solutions of the truncated system is compact in $H^1$ by the use of the so-called tail estimates.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45531718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dissipative reaction diffusion systems with polynomial growth","authors":"Takashi Suzuki","doi":"10.57262/ade/1580958059","DOIUrl":"https://doi.org/10.57262/ade/1580958059","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48307809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Large time asymptotics for the fractional nonlinear Schrödinger equation","authors":"N. Hayashi, P. Naumkin","doi":"10.57262/ade/1580958058","DOIUrl":"https://doi.org/10.57262/ade/1580958058","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44153800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：