Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications最新文献

{"title":"FULL DESCRIPTION OF THE SPECTRUM OF A STEKLOV-LIKE EIGENVALUE PROBLEM INVOLVING THE (p, q)-LAPLACIAN","authors":"L. Barbu, G. Morosanu","doi":"10.56082/annalsarscimath.2023.1-2.30","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.30","url":null,"abstract":"In this paper we consider in a bounded domain Q C RN a Steklov- like eigenvalue problem involving the (p, q)-Laplacian plus some poten­tials. Under suitable assumptions, using the Nehari manifold method and a variational approach, we are able to determine the full eigenvalue set of this problem as being an open interval (A*, +^) with A* > 0.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009552","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":"ON THE BANG-BANG PRINCIPLE FOR PARABOLIC OPTIMAL CONTROL PROBLEMS","authors":"F. Troltzsch","doi":"10.56082/annalsarscimath.2023.1-2.286","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.286","url":null,"abstract":"Optimal control problems for the linear heat equation with final observation and pointwise constraints on the control are considered, where the control depends only on the time. It is shown that to each finite number of given switching points, there is a final target such that the optimal objective value is positive, the optimal control is bang bang, and has the desired switching structure. The theory is completed by numerical examples.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009897","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":"IMPACT/CONTACT OF ELASTIC BODY ON A MOVING FOUNDATION","authors":"C. M. Murea","doi":"10.56082/annalsarscimath.2023.1-2.352","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.352","url":null,"abstract":"We study numerically the dynamic impact/contact of an elastic body on a moving foundation using the mid-point algorithm. Stability results are presented when foundation is decreasing. Numerical sim­ulations on two-dimensional problems are included and we show that the energy is absorbed in the case of decreasing foundation compared to the fixed one.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010119","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":"OPTIMAL TEMPERATURE DISTRIBUTION FOR A NONISOTHERMAL CAHN-HILLIARD SYSTEM IN TWO DIMENSIONS WITH SOURCE TERM AND DOUBLE OBSTACLE POTENTIAL","authors":"P. Colli, G. Gilardi, A. Signori, J. Sprekels","doi":"10.56082/annalsarscimath.2023.1-2.175","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.175","url":null,"abstract":"In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It couples a Cahn-Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier form, the con­stitutive law of the heat flux is assumed in the form given by the theory developed by Green and Naghdi, which accounts for a possible thermal memory of the evolution. This has the consequence that the balance law of internal energy becomes a second-order in time equation for the thermal displacement or freezing index, that is, a primitive with respect to time of the temperature. Another particular feature of our system is the presence of the source term in the equation for the order parameter, which entails further mathematical difficulties because the mass conservation of the order parameter is no longer satisfied. In this paper, we study the case that the double-well potential driving the evolution of the phase transition is given by the nondifferentiable dou­ble obstacle potential, thereby complementing recent results obtained for the differentiable cases of regular and logarithmic potentials. Be­sides existence results, we derive first-order necessary optimality condi­tions for the control problem. The analysis is carried out by employing the so-called deep quench approximation in which the nondifferentiable double obstacle potential is approximated by a family of potentials of logarithmic structure for which meaningful first-order necessary opti­mality conditions in terms of suitable adjoint systems and variational inequalities are available. Since the results for the logarithmic poten­tials crucially depend on the validity of the so-called strict separation property which is only available in the spatially two-dimensional situ­ation, our whole analysis is restricted to the two-dimensional case.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009888","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":"DAN TIBA AT HIS 70th ANNIVERSARY","authors":"Frederic Bonnans, Vasile Dragan","doi":"10.56082/annalsarscimath.2023.1-2.5","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.5","url":null,"abstract":"This issue is dedicated to the 70-th anniversary of Dan Tiba, a Romanian mathematician appreciated at the international level for his scientific contributions in the fields of optimization, optimal control for PDEs, shape and topology optimization, nonlinear analysis. His activity was marked by the passion for mathematics and his results were published by many prestigious journals and publishing houses. The colleagues and the collaborators wish him, at this anniversary moment, a long and active life in good health and more achievements in the mathematical research","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009890","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":"THREE WEAK FORMULATIONS FOR AN OBSTACLE MODEL AND THEIR RELATIONSHIP","authors":"A. Matei","doi":"10.56082/annalsarscimath.2023.1-2.408","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.408","url":null,"abstract":"We consider an obstacle model mathematically described by means of a boundary value problem governed by PDE. Three possible vari­ational formulations are highlighted. The first one is a variational inequality of the first kind and the other two are mixed variational for­mulations with Lagrange multipliers in dual spaces. After we discuss the solvability of the three variational formulations under consider­ation we focus on the relationship between them. Subsequently, we address the recovery of the formulation in terms of PDE starting from the mixed variational formulations.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010110","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":"DISSIPATION AND THE INFORMATION CONTENT OF THE DEVIATION FROM HAMILTONIAN DYNAMICS","authors":"M. Buliga","doi":"10.56082/annalsarscimath.2023.1-2.366","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.366","url":null,"abstract":"\"We explain a dissipative version of hamiltonian mechanics, based on the information content of the deviation from hamiltonian dynam¬ics. From this formulation we deduce minimal dissipation principles, dynamical inclusions, or constrained evolution with hamiltonian drift reformulations. Among applications we recover a dynamics generaliza¬tion of Mielke et al quasistatic rate-independent processes. This article gives a clear and unitary presentation of the theory of hamiltonian inclusions with convex dissipation or symplectic Brezis- Ekeland-Nayroles principle, presented under various conventions first in [3] arXiv:0810.1419, then in [4] arXiv:1408.3102 and, for the ap¬pearance of bipotentials in relation to the symplectic duality, in [2] arXiv:1902.04598v1.\"","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009900","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":"CONVERGENCE CRITERIA, WELL-POSEDNESS CONCEPTS AND APPLICATIONS","authors":"M. Sofonea, D.A. Tarzia","doi":"10.56082/annalsarscimath.2023.1-2.308","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.308","url":null,"abstract":"We consider an abstract problem P in a metric space X which has a unique solution u G X. Our aim in this current paper is two folds: first, to provide a convergence criterion to the solution of Problem P , that is, to give necessary and sufficient conditions on a sequence {un} C X which guarantee the convergence un ^ u in the space X; second, to find a Tyknonov triple T such that a sequence {un} C X is a T -approximating sequence if and only if it converges to u. The two problems stated above, associated to the original Problem P , are closely related. We illustrate how they can be solved in three particu­lar cases of Problem P: a variational inequality in a Hilbert space, a fixed point problem in a metric space and a minimization problem in a reflexive Banach space. For each of these problems we state and prove a convergence criterion that we use to define a convenient Tykhonov triple T which requires the condition stated above. We also show how the convergence criterion and the corresponding T -well posedness con­cept can be used to deduce convergence and classical well-posedness results, respectively.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009904","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":"CERTAIN ASPECTS OF Xrst(G)-CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES","authors":"O. Kiși, C. Choudhury","doi":"10.56082/annalsarscimath.2023.1-2.520","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.520","url":null,"abstract":"In the present article, we set forth with the new notion of rough A—statistical convergence in the gradual normed linear spaces. We produce significant results that present several fundamental properties of this notion. We also introduce the notion of Arst(G)—limit set and prove that it is convex, gradually closed, and plays an important role for the gradually A—statistical boundedness of a sequence.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009911","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":"SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.","authors":"H. A. Abass","doi":"10.56082/annalsarscimath.2023.1-2.535","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2023.1-2.535","url":null,"abstract":"In this paper, we study and introduce a self adaptive method to­gether with a Halpern iterative algorithm for approximating solutions of multiple-sets split monotone variational inclusion problem which in­cludes the multiple-sets split feasibility problem, split feasibility prob­lem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite-dimensional and infinite-dimensional spaces are displayed to illustrate the perfor­mance of our iterative method. The result discussed in this article extends and complements many related results in literature.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010115","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}