Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht, Thibaut Weller
{"title":"Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory","authors":"Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht, Thibaut Weller","doi":"10.21136/AM.2023.0013-23","DOIUrl":"10.21136/AM.2023.0013-23","url":null,"abstract":"<div><p>We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"25 - 48"},"PeriodicalIF":0.6,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74216655","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}
Mohammad Al Janaideh, Pavel Krejčí, Giselle Antunes Monteiro
{"title":"Inverse rate-dependent Prandtl-Ishlinskii operators and applications","authors":"Mohammad Al Janaideh, Pavel Krejčí, Giselle Antunes Monteiro","doi":"10.21136/AM.2023.0231-22","DOIUrl":"10.21136/AM.2023.0231-22","url":null,"abstract":"<div><p>In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent Prandtl-Ishlinskii operators to the case of a whole continuum of play operators with time-dependent thresholds. We prove the existence of an analytical inversion formula, and illustrate its applicability in the study of error bounds for inverse compensation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"713 - 726"},"PeriodicalIF":0.7,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82505233","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":"Exact controllability of linear dynamical systems: A geometrical approach","authors":"M. García-Planas","doi":"10.21136/AM.2016.0427-15","DOIUrl":"https://doi.org/10.21136/AM.2016.0427-15","url":null,"abstract":"In recent years there has been growing interest in the descriptive analysis of complex systems, permeating many aspects of daily life, obtaining considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems it is of interest to study the exact controllability; this measure is defined as the minimum set of controls that are needed in order to steer the whole system toward any desired state. In this paper, we focus the study on the obtention of the set of all B making the system (A, B) exact controllable.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"15 1","pages":"1-11"},"PeriodicalIF":0.7,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75302587","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 stability result for a class of nonlinear integrodifferential equations with L1 kernels","authors":"P. Cannarsa, D. Sforza","doi":"10.4064/AM35-4-2","DOIUrl":"https://doi.org/10.4064/AM35-4-2","url":null,"abstract":"We study the generation of analytic semigroups in the L-2 topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimensions, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type estimates for degenerate parabolic operators.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"2013 1","pages":"395-430"},"PeriodicalIF":0.7,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88068728","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":"Efficient robust estimation of time-series regression models","authors":"P. Čížek","doi":"10.2139/ssrn.1068624","DOIUrl":"https://doi.org/10.2139/ssrn.1068624","url":null,"abstract":"The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"7 1","pages":"267-279"},"PeriodicalIF":0.7,"publicationDate":"2007-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76390261","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":"70th birthday of Vratislav Horálek","authors":"V. Beneš, I. Saxl","doi":"10.21136/am.1996.134323","DOIUrl":"https://doi.org/10.21136/am.1996.134323","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"51 1 1","pages":"233-234"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90658065","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":"Combining the preconditioned conjugate gradient method and a matrix iterative method","authors":"J. Zítko","doi":"10.21136/am.1996.134311","DOIUrl":"https://doi.org/10.21136/am.1996.134311","url":null,"abstract":"Summary. The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated . The initial approxima tion for conjugate gradient is constructed as a result o f a matrix iteration method after 77i steps . The behaviour o f the error vector for such a combined method is studied and special numerical tests and conclusions are made.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"33 1","pages":"19-39"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73886114","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":"Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements","authors":"I. Hlavácek","doi":"10.21136/am.1996.134313","DOIUrl":"https://doi.org/10.21136/am.1996.134313","url":null,"abstract":"Hard clamped and hard simply supported elastic plate is considered. The mixed finite element analysis combined with some interpolation, proposed by Brezzi, Fortin and Stenberg, is extended to the case of variable thickness and anisotropic material.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"123 1","pages":"57-78"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83441022","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":"Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics","authors":"D. Goeleven","doi":"10.21136/AM.1996.134321","DOIUrl":"https://doi.org/10.21136/AM.1996.134321","url":null,"abstract":"This paper is devoted to the study of a class of hemivariational inequalities which was introduced by P. D. Panagiotopoulos [31] and later by Z. Naniewicz [22]. These variational formulations are natural nonconvex generalizations [15–17], [22–33] of the well-known variational inequalities. Several existence results are proved in [15]. In this paper, we are concerned with some related results and several applications.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"01 1","pages":"203-229"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88295563","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":"Finite element variational crimes in the case of semiregular elements","authors":"A. Ženíšek","doi":"10.21136/am.1996.134332","DOIUrl":"https://doi.org/10.21136/am.1996.134332","url":null,"abstract":"Till now the finite element analysis for semiregular finite elements has been restricted to interpolation theorems (see [2], [3], [5] and references there). In this paper a complete finite element analysis is presented briefly.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"44 1","pages":"367-398"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90126773","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}