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Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences 渐近概周期序列离散半群与空间的一致指数稳定性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1550
Nisar Ahmad, Habiba Khalid, A. Zada
{"title":"Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences","authors":"Nisar Ahmad, Habiba Khalid, A. Zada","doi":"10.4171/ZAA/1550","DOIUrl":"https://doi.org/10.4171/ZAA/1550","url":null,"abstract":"We prove that the discrete semigroup T = {T (n) : n ∈ Z+} is uniformly exponentially stable if and only if for each z(n) ∈ AAP0(Z+,X ) the solution of the Cauchy problem { yn+1 = T (1)yn + z(n + 1), y(0) = 0 belongs to AAP0(Z+,X ). Where T (1) is the algebraic generator of T, Z+ is the set of all non-negative integers and X is a complex Banach space. Our proof uses the approach of discrete evolution semigroups.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81471010","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}
引用次数: 4
Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability 线性运动硬化拟静态塑性的最优控制II:正则化与可微性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1546
G. Wachsmuth
{"title":"Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability","authors":"G. Wachsmuth","doi":"10.4171/ZAA/1546","DOIUrl":"https://doi.org/10.4171/ZAA/1546","url":null,"abstract":"We consider an optimal control problem governed by an evolution variational inequality arising in quasistatic plasticity with linear kinematic hardening. A regularization of the time-discrete problem is derived. The regularized forward problem can be interpreted as system of coupled quasilinear PDEs whose principal parts depend on the gradient of the state. We show the Fréchet differentiability of the solution map of this quasilinear system. As a consequence, we obtain a first order necessary optimality system. Moreover, we address certain convergence properties of the regularization.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86786067","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}
引用次数: 23
A Characterization of Absolute Continuity by means of Mellin Integral Operators 用Mellin积分算子描述绝对连续性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-07-08 DOI: 10.4171/ZAA/1543
L. Angeloni, G. Vinti
{"title":"A Characterization of Absolute Continuity by means of Mellin Integral Operators","authors":"L. Angeloni, G. Vinti","doi":"10.4171/ZAA/1543","DOIUrl":"https://doi.org/10.4171/ZAA/1543","url":null,"abstract":"In the case of classical convolution operators, an important characterization of absolute continuity is given in terms of convergence in variation. In this paper we will study this problem for Mellin integral operators, proving analogous characterizations in the frame of the classical BV -spaces, both in the one-dimensional and in the multidimensional setting.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85958307","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}
引用次数: 15
Density results for energy spaces on some fractafolds 一些分形折叠上能量空间的密度结果
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-07-08 DOI: 10.4171/ZAA/1544
M. R. Lancia, Valerio Regis Durante, P. Vernole
{"title":"Density results for energy spaces on some fractafolds","authors":"M. R. Lancia, Valerio Regis Durante, P. Vernole","doi":"10.4171/ZAA/1544","DOIUrl":"https://doi.org/10.4171/ZAA/1544","url":null,"abstract":". In this paper we prove density results for the domains of energy forms defined on a scale irregular fractal surface S ( (cid:24) ) , as well as on the corresponding three-dimensional bounded cylindrical domain Q ( (cid:24) ) , whose lateral boundary is S ( (cid:24) ) .","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86337006","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}
引用次数: 8
Variational-hemivariational approach to a quasistatic viscoelastic problem with normal compliance, friction and material damage 具有正常柔度、摩擦和材料损伤的准静态粘弹性问题的变分-半变分方法
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-07-08 DOI: 10.4171/ZAA/1538
L. Gasiński, A. Ochal, M. Shillor
{"title":"Variational-hemivariational approach to a quasistatic viscoelastic problem with normal compliance, friction and material damage","authors":"L. Gasiński, A. Ochal, M. Shillor","doi":"10.4171/ZAA/1538","DOIUrl":"https://doi.org/10.4171/ZAA/1538","url":null,"abstract":"This work studies a model for quasistatic frictional contact between a viscoelastic body and a reactive foundation. The constitutive law is assumed to be nonlinear and contains damage effects modeled by a parabolic differential inclusion. Contact is described by the normal compliance condition and a subdifferential frictional condition. A variational-hemivariational formulation of the problem is provided and the existence and uniqueness of its solution is proved. The proof is based on a surjectivity result for pseudomonotone coercive operators and a fixed point argument.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88262280","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}
引用次数: 11
Multiplicity of Nontrivial Solutions of a Class of Fractional $p$-Laplacian Problem 一类分数阶$p$-拉普拉斯问题非平凡解的多重性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-07-08 DOI: 10.4171/ZAA/1541
Ghanmi Abdeljabbar
{"title":"Multiplicity of Nontrivial Solutions of a Class of Fractional $p$-Laplacian Problem","authors":"Ghanmi Abdeljabbar","doi":"10.4171/ZAA/1541","DOIUrl":"https://doi.org/10.4171/ZAA/1541","url":null,"abstract":". In this paper, we deal with existence of nontrivial solutions to the fractional p -Laplacian problem of the type where Ω is a bounded domain in R n with smooth boundary ∂ Ω, a ∈ C (Ω), p ≥ 2, α ∈ (0 , 1) such that pα < n , 1 < q < p < r < npn − αp , and F ∈ C 1 (Ω × R , R ). Using the decomposition of the Nehari manifold, we prove that the non-local elliptic problem has at least two nontrivial solutions.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83424282","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}
引用次数: 12
Local Well-Posedness of a Coupled Camassa-Holm System in Critical Spaces 临界空间中耦合Camassa-Holm系统的局部适定性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-01-08 DOI: 10.4171/ZAA/1528
Xingxing Liu
{"title":"Local Well-Posedness of a Coupled Camassa-Holm System in Critical Spaces","authors":"Xingxing Liu","doi":"10.4171/ZAA/1528","DOIUrl":"https://doi.org/10.4171/ZAA/1528","url":null,"abstract":". In this paper, we consider the local well-posedness of a coupled Camassa-Holm system with initial data in Besov spaces B s 2 1 with critical index s = 32 .","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77538251","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}
引用次数: 2
Existence of Homoclinic Orbits of Superquadratic Second-Order Hamiltonian Systems 超二次二阶哈密顿系统同斜轨道的存在性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-01-08 DOI: 10.4171/ZAA/1527
Chengjun Guo, D. O’Regan, Chengjiang Wang, R. Agarwal
{"title":"Existence of Homoclinic Orbits of Superquadratic Second-Order Hamiltonian Systems","authors":"Chengjun Guo, D. O’Regan, Chengjiang Wang, R. Agarwal","doi":"10.4171/ZAA/1527","DOIUrl":"https://doi.org/10.4171/ZAA/1527","url":null,"abstract":"Using critical point theory, we study the existence of homoclinic orbits for the second-order Hamiltonian system z̈ −Kz(t, z) + Vz(t, z) = h(t), where V (t, z) depends periodically on t and is superquadratic.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77984086","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}
引用次数: 13
Interpolation of Closed Subspaces and Invertibility of Operators 闭子空间的插值与算子的可逆性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-01-08 DOI: 10.4171/ZAA/1525
I. Asekritova, F. Cobos, N. Kruglyak
{"title":"Interpolation of Closed Subspaces and Invertibility of Operators","authors":"I. Asekritova, F. Cobos, N. Kruglyak","doi":"10.4171/ZAA/1525","DOIUrl":"https://doi.org/10.4171/ZAA/1525","url":null,"abstract":"Let (Y0, Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj ; (j = 0; 1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (θ, q) such that the real interpolation space (X0, X1)θ, q is a closed subspace of (Y0, Y1)θ, q : In particular, we establish conditions which are necessary and sufficient for the equality (X0, X1)θ, q =(Y0, Y1)θ, q, with the proof based on a previous result by Asekritova and Kruglyak on invertibility of operators. We also generalize the theorem by Ivanov and Kalton where this problem was solved under several rather restrictive conditions, such as that X1 = Y1 and X0 is a subspace of codimension one in Y0","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90626588","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}
引用次数: 3
On the Well-Posedness of the Boussinesq Equations with Anisotropic Filter for Turbulent Flows 紊流各向异性滤波器Boussinesq方程的适定性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-01-08 DOI: 10.4171/ZAA/1529
L. Berselli, D. Catania
{"title":"On the Well-Posedness of the Boussinesq Equations with Anisotropic Filter for Turbulent Flows","authors":"L. Berselli, D. Catania","doi":"10.4171/ZAA/1529","DOIUrl":"https://doi.org/10.4171/ZAA/1529","url":null,"abstract":"We consider approximate deconvolution models for the Boussinesq equations, based on suitable anisotropic filters. We discuss existence and well-posedness of the solutions, with particular emphasis on the role of the energy (of the model) balance.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87014594","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}
引用次数: 8
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