We perform the asymptotic analysis of the scalar advection-diffusion equation y e t −ey e xx +M y e x = 0, (x, t) ∈ (0, 1) × (0, T), with respect to the diffusion coefficient e. We use the matched asymptotic expansion method which allows to describe the boundary layers of the solution. We then use the asymptotics to discuss the controllability property of the solution for T ≥ 1/M .
我们对标量平流扩散方程ye t - ey e xx +M ye x = 0， (x, t)∈(0,1)x (0, t)关于扩散系数e进行渐近分析。我们使用匹配渐近展开方法，该方法允许描述解的边界层。然后利用渐近性讨论了T≥1/M时解的可控性。
{"title":"Asymptotic analysis of an advection-diffusion equation and application to boundary controllability","authors":"Y. Amirat, A. Münch","doi":"10.3233/ASY-181497","DOIUrl":"https://doi.org/10.3233/ASY-181497","url":null,"abstract":"We perform the asymptotic analysis of the scalar advection-diffusion equation y e t −ey e xx +M y e x = 0, (x, t) ∈ (0, 1) × (0, T), with respect to the diffusion coefficient e. We use the matched asymptotic expansion method which allows to describe the boundary layers of the solution. We then use the asymptotics to discuss the controllability property of the solution for T ≥ 1/M .","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"60 8 1","pages":"59-106"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86801766","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}
{"title":"Spectral non-self-adjoint analysis of complex Dirac, Pauli and Schrödinger operators with constant magnetic fields of full rank","authors":"D. Sambou","doi":"10.3233/ASY-181491","DOIUrl":"https://doi.org/10.3233/ASY-181491","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"7 1","pages":"113-136"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81082971","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}
S. Shmarev, J. Simsen, M. S. Simsen, M. Tovani-Palone
{"title":"Asymptotic behavior for a class of parabolic equations in weighted variable Sobolev spaces","authors":"S. Shmarev, J. Simsen, M. S. Simsen, M. Tovani-Palone","doi":"10.3233/ASY-181486","DOIUrl":"https://doi.org/10.3233/ASY-181486","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"18 1","pages":"43-68"},"PeriodicalIF":0.0,"publicationDate":"2018-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88841158","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}
This paper deals with homogenization of parabolic problems for integral convolution type operators with a non-symmetric jump kernel in a periodic elliptic medium. It is shown that the homogenization result holds in moving coordinates. We determine the corresponding effective velocity and prove that the limit operator is a second order parabolic operator with constant coefficients. We also consider the behaviour of the effective velocity in the case of small antisymmetric perturbations of a symmetric kernel.
{"title":"Homogenization of biased convolution type operators","authors":"Andrey L. Piatnitski, E. Zhizhina","doi":"10.3233/asy-191533","DOIUrl":"https://doi.org/10.3233/asy-191533","url":null,"abstract":"This paper deals with homogenization of parabolic problems for integral convolution type operators with a non-symmetric jump kernel in a periodic elliptic medium. It is shown that the homogenization result holds in moving coordinates. We determine the corresponding effective velocity and prove that the limit operator is a second order parabolic operator with constant coefficients. We also consider the behaviour of the effective velocity in the case of small antisymmetric perturbations of a symmetric kernel.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"49 1","pages":"241-262"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88889264","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}
James C. Robinson, José L. Rodrigo, Jack W. D. Skipper
We study weak solutions of the incompressible Euler equations on T2×R+; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove energy conservation under the assumptions that u∈L3(0,T;L3(T2×R+)), lim|y|→01|y|∫0T∫T2∫x3>|y|∞|u(x+y)−u(x)|3dxdt=0, and an additional continuity condition near the boundary: for some δ>0 we require u∈L3(0,T;C0(T2×[0,δ])). We note that all our conditions are satisfied whenever u(x,t)∈Cα, for some α>1/3, with Holder constant C(x,t)∈L3(T2×R+×(0,T)).
研究了T2×R+上不可压缩欧拉方程的弱解;我们使用无散度且法向分量为零的测试函数，从而得到一个不涉及压力的定义。我们在u∈L3(0,T;L3(T2×R+))， lim|y|→01|y|∫0T∫T2∫x3>|y|∞|u(x+y)−u(x)|3dxdt=0的假设下证明了能量守恒，并在边界附近证明了一个附加的连续性条件:对于某些δ>0，我们要求u∈L3(0,T;C0(t2x [0，δ]))。我们注意到，当u(x,t)∈Cα，对于某些α>1/3，且Holder常数C(x,t)∈L3(T2×R+ x (0, t))时，所有条件都满足。
{"title":"Energy conservation for the Euler equations on T2×R+ for weak solutions defined without reference to the pressure","authors":"James C. Robinson, José L. Rodrigo, Jack W. D. Skipper","doi":"10.3233/ASY-181482","DOIUrl":"https://doi.org/10.3233/ASY-181482","url":null,"abstract":"We study weak solutions of the incompressible Euler equations on T2×R+; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove energy conservation under the assumptions that u∈L3(0,T;L3(T2×R+)), lim|y|→01|y|∫0T∫T2∫x3>|y|∞|u(x+y)−u(x)|3dxdt=0, and an additional continuity condition near the boundary: for some δ>0 we require u∈L3(0,T;C0(T2×[0,δ])). We note that all our conditions are satisfied whenever u(x,t)∈Cα, for some α>1/3, with Holder constant C(x,t)∈L3(T2×R+×(0,T)).","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"19 1","pages":"185-202"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90167895","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}
with g : [0,+∞) → [0,+∞) increasing and bounded. The approximating functionals are of AmbrosioTortorelli type and depend on the Hessian or on the Laplacian of the edge variable v which thus belongs to W (Ω). When the space dimension is equal to two and three v is then continuous and this improved regularity leads to a sequence of approximating functionals which are ready to be used for numerical simulations.
{"title":"Second-order approximation of free-discontinuity problems with linear growth","authors":"Teresa Esposito","doi":"10.3233/ASY-181476","DOIUrl":"https://doi.org/10.3233/ASY-181476","url":null,"abstract":"with g : [0,+∞) → [0,+∞) increasing and bounded. The approximating functionals are of AmbrosioTortorelli type and depend on the Hessian or on the Laplacian of the edge variable v which thus belongs to W (Ω). When the space dimension is equal to two and three v is then continuous and this improved regularity leads to a sequence of approximating functionals which are ready to be used for numerical simulations.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"5 1","pages":"21-52"},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73656968","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}
We provide complete structural theorems for the so-called quasiasymptotic behavior of ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ultradistributions and discuss connections with Gelfand-Shilov spaces.
{"title":"Structural theorems for quasiasymptotics of ultradistributions","authors":"L. Neyt, J. Vindas","doi":"10.3233/ASY-181514","DOIUrl":"https://doi.org/10.3233/ASY-181514","url":null,"abstract":"We provide complete structural theorems for the so-called quasiasymptotic behavior of ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ultradistributions and discuss connections with Gelfand-Shilov spaces.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"142 1","pages":"1-18"},"PeriodicalIF":0.0,"publicationDate":"2018-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76208293","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}
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：