Pub Date : 2023-07-19DOI: 10.1007/s40306-023-00507-3
Timothée Raoul Moutngui See, Pierre Noundjeu
In this paper we prove the existence of initial data satisfying the constraint equations corresponding to the 1+3 formulation of asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system, when the charge of the particles is either low or large, the initial distribution function is compactly supported, the shift vector is non-zero and the isotropic metric ansatz is not diagonal. This result extends the work (Rein and Rendall, Commun. Math. Phys. 150(3), 561–583 1992) concerning the existence of solutions to the constraint equations for chargeless particles.
{"title":"The Constraint Equations of the Einstein-Vlasov-Maxwell System in the Maximal-isotropic Coordinates","authors":"Timothée Raoul Moutngui See, Pierre Noundjeu","doi":"10.1007/s40306-023-00507-3","DOIUrl":"10.1007/s40306-023-00507-3","url":null,"abstract":"<div><p>In this paper we prove the existence of initial data satisfying the constraint equations corresponding to the 1+3 formulation of asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system, when the charge of the particles is either low or large, the initial distribution function is compactly supported, the shift vector is non-zero and the isotropic metric ansatz is not diagonal. This result extends the work (Rein and Rendall, Commun. Math. Phys. <b>150</b>(3), 561–583 1992) concerning the existence of solutions to the constraint equations for chargeless particles.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00507-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47283373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-18DOI: 10.1007/s40306-023-00508-2
Le Huynh My Van, Dang Le Thuy, Tran Viet Anh
In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.
{"title":"Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces","authors":"Le Huynh My Van, Dang Le Thuy, Tran Viet Anh","doi":"10.1007/s40306-023-00508-2","DOIUrl":"10.1007/s40306-023-00508-2","url":null,"abstract":"<div><p>In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48474134","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}
Pub Date : 2023-07-17DOI: 10.1007/s40306-023-00505-5
Kaituo Liu, Jianzhong Lu, Lihua Peng
In this paper, we establish a decomposition theorem for strong martingale Hardy space (sH_p^sigma ), which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between (sH_p^sigma ;(0<ple 1)) and (sL_2). Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.
{"title":"Real Interpolation Between Strong Martingale Hardy Spaces","authors":"Kaituo Liu, Jianzhong Lu, Lihua Peng","doi":"10.1007/s40306-023-00505-5","DOIUrl":"10.1007/s40306-023-00505-5","url":null,"abstract":"<div><p>In this paper, we establish a decomposition theorem for strong martingale Hardy space <span>(sH_p^sigma )</span>, which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between <span>(sH_p^sigma ;(0<ple 1))</span> and <span>(sL_2)</span>. Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46630442","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}
Pub Date : 2023-07-11DOI: 10.1007/s40306-023-00506-4
Anurag K. Singh, Kei-ichi Watanabe
We study the behavior of various properties of commutative Noetherian rings under Segre products, with a special focus on properties in positive prime characteristic defined using the Frobenius endomorphism. Specifically, we construct normal graded rings of finite Frobenius representation type that are not Cohen-Macaulay.
{"title":"On Segre Products, F-regularity, and Finite Frobenius Representation Type","authors":"Anurag K. Singh, Kei-ichi Watanabe","doi":"10.1007/s40306-023-00506-4","DOIUrl":"10.1007/s40306-023-00506-4","url":null,"abstract":"<div><p>We study the behavior of various properties of commutative Noetherian rings under Segre products, with a special focus on properties in positive prime characteristic defined using the Frobenius endomorphism. Specifically, we construct normal graded rings of finite Frobenius representation type that are not Cohen-Macaulay.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45511127","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-24pt study the nonlinear stochastic time-fractional diffusion equation in the spatial domain (mathbb {R}) driven by a locally Lipschitz source satisfying
where (xin mathbb {R},alpha in (0,1],gamma ge 1-alpha ), the source term is defined (F(t,x,u) = f(t,x,u(t,x)))( + rho (t,x,u(t,x))dot{W}(t,x)) and W is the multiplicative space-time white noise. We investigate the existence, uniqueness of a maximal random field solution. Moreover, we prove the stability of the solution with respect to perturbed fractional orders (alpha , gamma ) and the initial condition.
{"title":"Continuity of the Solution to a Stochastic Time-fractional Diffusion Equations in the Spatial Domain with Locally Lipschitz Sources","authors":"Dang Duc Trong, Nguyen Dang Minh, Nguyen Nhu Lan, Nguyen Thi Mong Ngoc","doi":"10.1007/s40306-023-00503-7","DOIUrl":"10.1007/s40306-023-00503-7","url":null,"abstract":"<div><p>We-24pt study the nonlinear stochastic time-fractional diffusion equation in the spatial domain <span>(mathbb {R})</span> driven by a locally Lipschitz source satisfying </p><div><div><span>$$begin{aligned} left( {~}_{t}D_{0^{+}}^{alpha } - frac{partial ^{2} }{partial x^{2}}right) u(t,x) = I_{t}^{gamma }left( F(t,x,u)right) , end{aligned}$$</span></div></div><p>where <span>(xin mathbb {R},alpha in (0,1],gamma ge 1-alpha )</span>, the source term is defined <span>(F(t,x,u) = f(t,x,u(t,x)))</span> <span>( + rho (t,x,u(t,x))dot{W}(t,x))</span> and <i>W</i> is the multiplicative space-time white noise. We investigate the existence, uniqueness of a maximal random field solution. Moreover, we prove the stability of the solution with respect to perturbed fractional orders <span>(alpha , gamma )</span> and the initial condition.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00503-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48136681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-20DOI: 10.1007/s40306-023-00500-w
Loc H. Nguyen
We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the PDE under consideration. To find this fixed point, we define a recursive sequence with an arbitrary initial term using the same manner as in the proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution. On the other hand, we also show that our method delivers reliable solutions even when the given data are noisy. Numerical examples are presented.
{"title":"The Carleman Contraction Mapping Method for Quasilinear Elliptic Equations with Over-determined Boundary Data","authors":"Loc H. Nguyen","doi":"10.1007/s40306-023-00500-w","DOIUrl":"10.1007/s40306-023-00500-w","url":null,"abstract":"<div><p>We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the PDE under consideration. To find this fixed point, we define a recursive sequence with an arbitrary initial term using the same manner as in the proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution. On the other hand, we also show that our method delivers reliable solutions even when the given data are noisy. Numerical examples are presented.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00500-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43053841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-05DOI: 10.1007/s40306-023-00498-1
Hichame Amal, Saïd Asserda, Manar Bouhssina
Let (X,ω) be an n-dimensional compact Kähler manifold and fix an integer m such that 1 ≤ m ≤ n. Let μ be a finite Borel measure on X satisfying the conditions ({mathscr{H}}_{m}(delta , A,omega )). We study degenerate complex Hessian equations of the form (ω + ddcφ)m ∧ ωn−m = F(φ,.)dμ. Under some natural conditions on F, we prove that if (0<delta <frac {m}{n-m}), then this equation has a unique continuous solution.
{"title":"Continuous Solutions for Degenerate Complex Hessian Equation","authors":"Hichame Amal, Saïd Asserda, Manar Bouhssina","doi":"10.1007/s40306-023-00498-1","DOIUrl":"10.1007/s40306-023-00498-1","url":null,"abstract":"<div><p>Let (<i>X</i>,<i>ω</i>) be an <i>n</i>-dimensional compact Kähler manifold and fix an integer <i>m</i> such that 1 ≤ <i>m</i> ≤ <i>n</i>. Let <i>μ</i> be a finite Borel measure on <i>X</i> satisfying the conditions <span>({mathscr{H}}_{m}(delta , A,omega ))</span>. We study degenerate complex Hessian equations of the form (<i>ω</i> + <i>d</i><i>d</i><sup><i>c</i></sup><i>φ</i>)<sup><i>m</i></sup> ∧ <i>ω</i><sup><i>n</i>−<i>m</i></sup> = <i>F</i>(<i>φ</i>,.)<i>d</i><i>μ</i>. Under some natural conditions on <i>F</i>, we prove that if <span>(0<delta <frac {m}{n-m})</span>, then this equation has a unique continuous solution.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00498-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50450333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-21DOI: 10.1007/s40306-023-00496-3
Le Thi Phuong Ngoc, Nguyen Anh Triet, Phan Thi My Duyen, Nguyen Thanh Long
In this paper, we investigate the Robin-Dirichlet problem for a nonlinear pseudoparabolic equation of Kirchhoff-Carrier type with viscoelastic term. Under suitable assumptions on the initial data and the relaxation function included in the viscoelastic term, we obtain sufficient conditions for the existence, uniqueness, blow-up, and decay of a weak solution. The results obtained here extend the ones in a previous paper of the authors (Ngoc et al., Math. Meth. Appl. Sci.44(11), 8697–8725, 26).
{"title":"General Decay and Blow-up Results of a Robin-Dirichlet Problem for a Pseudoparabolic Nonlinear Equation of Kirchhoff-Carrier Type with Viscoelastic Term","authors":"Le Thi Phuong Ngoc, Nguyen Anh Triet, Phan Thi My Duyen, Nguyen Thanh Long","doi":"10.1007/s40306-023-00496-3","DOIUrl":"10.1007/s40306-023-00496-3","url":null,"abstract":"<div><p>In this paper, we investigate the Robin-Dirichlet problem for a nonlinear pseudoparabolic equation of Kirchhoff-Carrier type with viscoelastic term. Under suitable assumptions on the initial data and the relaxation function included in the viscoelastic term, we obtain sufficient conditions for the existence, uniqueness, blow-up, and decay of a weak solution. The results obtained here extend the ones in a previous paper of the authors (Ngoc et al., <i>Math. Meth. Appl. Sci.</i> <b>44</b>(11), 8697–8725, 26).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47518408","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}