Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00023-5
Asim Ilyas, Salman A. Malik, Kamran Suhaib
We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided.
{"title":"IDENTIFYING DIFFUSION CONCENTRATION AND SOURCE TERM FOR ANOMALOUS DIFFUSION EQUATION","authors":"Asim Ilyas, Salman A. Malik, Kamran Suhaib","doi":"10.1016/S0034-4877(24)00023-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00023-5","url":null,"abstract":"<div><p>We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A model of nonlinear elastic media containing cavities, microcracks, or soft inclusions is considered. We propose a modification of the well-known model to such media. The modification consists in taking into account those terms in the approximate equation of state that were discarded in the previously considered models. The main goal of the ongoing research is to show the persistence of the soliton-like solutions in the modified model, and to study their dynamical properties.
{"title":"ON THE SOLITON-LIKE SOLUTIONS OF THE REFINED MODEL OF ELASTIC MEDIA CONTAINING INCLUSIONS","authors":"Lucjan Sapa, Sergii Skurativskyi, Vsevolod Vladimirov","doi":"10.1016/S0034-4877(24)00024-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00024-7","url":null,"abstract":"<div><p>A model of nonlinear elastic media containing cavities, microcracks, or soft inclusions is considered. We propose a modification of the well-known model to such media. The modification consists in taking into account those terms in the approximate equation of state that were discarded in the previously considered models. The main goal of the ongoing research is to show the persistence of the soliton-like solutions in the modified model, and to study their dynamical properties.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00022-3
Gunwoo Cho, Jimyeong Kim, Ihyeok Seo, Seongyeon Kim, Yehyun Kwon
We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [16] and Rodnianski [18] on the free Schrödinger evolution to the general case regarding potentials.
{"title":"QUANTUM REVIVALS AND FRACTALITY FOR THE SCHRÖDINGER EQUATION","authors":"Gunwoo Cho, Jimyeong Kim, Ihyeok Seo, Seongyeon Kim, Yehyun Kwon","doi":"10.1016/S0034-4877(24)00022-3","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00022-3","url":null,"abstract":"<div><p>We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [<span>16</span>] and Rodnianski [<span>18</span>] on the free Schrödinger evolution to the general case regarding potentials.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00026-0
Mona Khare, Ravi Singh Chauhan
In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (P, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (P, μ) is chain mixing, then φn is chain transitive for each n ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (P, μ, φ) under suitable conditions. Examples are given to support the theory.
本文研究了量子度量空间(P,μ)动力学中的链传递性、ε阴影和广延性概念。除了证明了链传递性量子动力学系统的几个结果之外,还证明了如果(P, μ)上的度量保持态φ是链混合的,那么对于每个 n ∊ ℕ,φn 都是链传递性的。本研究还阐明了量子动力学系统(P, μ, φ)在适当条件下的ε阴影和扩张性之间的相互关系。举例说明了这一理论。
{"title":"CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS","authors":"Mona Khare, Ravi Singh Chauhan","doi":"10.1016/S0034-4877(24)00026-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00026-0","url":null,"abstract":"<div><p>In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (<em>P</em>, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (<em>P</em>, μ) is chain mixing, then φ<sup><em>n</em></sup> is chain transitive for each <em>n</em> ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (<em>P</em>, μ, φ) under suitable conditions. Examples are given to support the theory.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00029-6
Qianqian Xia
We study singular reduction of contact Hamiltonian systems acted upon properly by a Lie group. The tools we use are the category of differential space.
我们研究由一个李群适当作用的接触哈密顿系统的奇异还原。我们使用的工具是微分空间范畴。
{"title":"SINGULAR REDUCTION OF CONTACT HAMILTONIAN SYSTEMS","authors":"Qianqian Xia","doi":"10.1016/S0034-4877(24)00029-6","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00029-6","url":null,"abstract":"<div><p>We study singular reduction of contact Hamiltonian systems acted upon properly by a Lie group. The tools we use are the category of differential space.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00025-9
Mansur I. Ismailov, Muhammed Çiçek
The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.
{"title":"INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION","authors":"Mansur I. Ismailov, Muhammed Çiçek","doi":"10.1016/S0034-4877(24)00025-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00025-9","url":null,"abstract":"<div><p>The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00027-2
Pooja Soni, Manju Pruthi, Arun Kumar Yadav
This research paper discusses the construction of novel and better quantum codes from the direct product of t-copies of ring R (discussed in Section 2), using cyclic codes over R by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring R. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.
本研究论文讨论了通过使用 CSS 构建技术,利用环 R 上的循环码,从环 R 的 t 副本的直接乘积(在第 2 节中讨论)构建新颖且更好的量子编码。此外,我们在第 2.1 小节中分析了格雷映射的距离保留性质。在这里,我们还利用量子单子缺陷(QSD)的概念研究了最大距离可分离(MDS)编码,它表示编码的整体质量。为了证明我们研究结果的实用性,我们提供了使用 Magma 软件实现的示例。
{"title":"NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING","authors":"Pooja Soni, Manju Pruthi, Arun Kumar Yadav","doi":"10.1016/S0034-4877(24)00027-2","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00027-2","url":null,"abstract":"<div><p>This research paper discusses the construction of novel and better quantum codes from the direct product of <em>t</em>-copies of ring <em>R</em> (discussed in Section 2), using cyclic codes over <em>R</em> by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring <em>R</em>. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1016/S0034-4877(24)00028-4
Shahroud Azami, Mehdi Jafari
In the present paper, we investigate the 3-dimensional Lie group (ℍ2 × ℝ, g) where g is a left-invariant Riemannian metric and we determine the Ricci solitons and Ricci bi-conformal vector fields on it.
在本文中,我们研究了三维李群(ℍ2 × ℝ,g),其中 g 是左不变黎曼度量,并确定了其上的利玛窦孤子和利玛窦双共形矢量场。
{"title":"RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE LIE GROUP ℍ2 × ℝ","authors":"Shahroud Azami, Mehdi Jafari","doi":"10.1016/S0034-4877(24)00028-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00028-4","url":null,"abstract":"<div><p>In the present paper, we investigate the 3-dimensional Lie group (ℍ<sup>2</sup> × ℝ, <em>g</em>) where <em>g</em> is a left-invariant Riemannian metric and we determine the Ricci solitons and Ricci bi-conformal vector fields on it.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-01DOI: 10.1016/S0034-4877(24)00008-9
Saeed ur Rahman, José Luis Díaz Palencia
The purpose of the presented article is to develop some new global regularity criteria for a magnetohydrodynamic (MHD) fluid flowing in a saturated porous medium. The effect of the porous medium, over the fluid flow, is characterized by a Darcy–Forchheimer law. The fluid, under study, is considered as one-dimensional and flowing in the x–direction with velocity component u. In addition, such a component is assumed to vary with the y–direction, i.e. u(y). Then, given the vorticity function , such that is sufficiently small, we develop the regularity criteria under the scope of the L2 space. We extend our results to the spaces Ls, where s > 2. Afterward, we prove the Liouville-type theorem for the MHD Darcy–Forchheimer flow equation. Eventually, we obtain some characterization about the asymptotic behaviour of solutions, particularly, the nonuniform convergence in L2 for .
{"title":"New regularity criteria for an MHD Darcy-Forchheimer fluid","authors":"Saeed ur Rahman, José Luis Díaz Palencia","doi":"10.1016/S0034-4877(24)00008-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00008-9","url":null,"abstract":"<div><p>The purpose of the presented article is to develop some new global regularity criteria for a magnetohydrodynamic (MHD) fluid flowing in a saturated porous medium. The effect of the porous medium, over the fluid flow, is characterized by a Darcy–Forchheimer law. The fluid, under study, is considered as one-dimensional and flowing in the <em>x–</em>direction with velocity component <em>u.</em> In addition, such a component is assumed to vary with the <em>y–</em>direction, i.e. <em>u</em>(<em>y</em>). Then, given the vorticity function\u0000<span><math><mrow><mi>w</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>y</mi></mrow></mfrac></mrow></math></span>, such that\u0000<span><math><mrow><msubsup><mrow><mrow><mo>‖</mo><mi>w</mi><mo>‖</mo></mrow></mrow><mrow><mtext>BMO</mtext></mrow><mn>2</mn></msubsup></mrow></math></span> is sufficiently small, we develop the regularity criteria under the scope of the <em>L</em><sup>2</sup> space. We extend our results to the spaces <em>L<sup>s</sup></em>, where <em>s</em> > 2. Afterward, we prove the Liouville-type theorem for the MHD Darcy–Forchheimer flow equation. Eventually, we obtain some characterization about the asymptotic behaviour of solutions, particularly, the nonuniform convergence in <em>L</em><sup>2</sup> for\u0000<span><math><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></math></span>.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000089/pdfft?md5=0d1891c76d0aee709cdeee928726e3d4&pid=1-s2.0-S0034487724000089-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-01DOI: 10.1016/S0034-4877(24)00007-7
Marián Fecko
The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics.
{"title":"Galilean and Carrollian Hodge star operators","authors":"Marián Fecko","doi":"10.1016/S0034-4877(24)00007-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00007-7","url":null,"abstract":"<div><p>The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000077/pdfft?md5=95dc18d8cfd864d5e9758bc25b1ea4dd&pid=1-s2.0-S0034487724000077-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}