. The uniform stabilization of a semilinear wave equation with variable coef-ficients and nonlinear boundary conditions is considered. The uniform decay rate is established by the Riemannian geometry method.
。研究一类具有非线性边界条件的变系数半线性波动方程的一致镇定问题。用黎曼几何方法建立了均匀衰减率。
{"title":"Uniform Stabilization for a Semilinear Wave Equation with Variable Coefficients and Nonlinear Boundary Conditions","authors":"El-Hadi Kamel, A. Ainouz, A. Khemmoudj","doi":"10.11650/tjm/220302","DOIUrl":"https://doi.org/10.11650/tjm/220302","url":null,"abstract":". The uniform stabilization of a semilinear wave equation with variable coef-ficients and nonlinear boundary conditions is considered. The uniform decay rate is established by the Riemannian geometry method.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46351763","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":"Blow-up in Coupled Solutions for a $4$-dimensional Semilinear Elliptic Kuramoto–Sivashinsky System","authors":"Lilia Larbi, N. Trabelsi","doi":"10.11650/tjm/220601","DOIUrl":"https://doi.org/10.11650/tjm/220601","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44998661","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}
. In this paper, we concentrate on the generalized multiple-set split feasibility problems in Hilbert spaces and propose a new iterative method for this problem. One of the most important of this method is using dynamic step-sizes, in which the information of the previous step is the only requirement to compute the next approximation. The strong convergence result of the suggested algorithm is proven theoretically under some feasible assumptions. When considering the main results in some special cases, we also obtain some applications regarding the solution of the multiple-set split feasibility problem, the split feasibility problem with multiple output sets, and the split feasibility problem as well as the linear optimal control problem. Some numerical experiments on infinite-dimensional spaces and applications in optimal control problems are conducted to demonstrate the advantages and computational efficiency of the proposed algorithms over some existing results.
{"title":"A Parallel Algorithm for Generalized Multiple-set Split Feasibility with Application to Optimal Control Problems","authors":"N. T. Thuy, N. T. Nghia","doi":"10.11650/tjm/220502","DOIUrl":"https://doi.org/10.11650/tjm/220502","url":null,"abstract":". In this paper, we concentrate on the generalized multiple-set split feasibility problems in Hilbert spaces and propose a new iterative method for this problem. One of the most important of this method is using dynamic step-sizes, in which the information of the previous step is the only requirement to compute the next approximation. The strong convergence result of the suggested algorithm is proven theoretically under some feasible assumptions. When considering the main results in some special cases, we also obtain some applications regarding the solution of the multiple-set split feasibility problem, the split feasibility problem with multiple output sets, and the split feasibility problem as well as the linear optimal control problem. Some numerical experiments on infinite-dimensional spaces and applications in optimal control problems are conducted to demonstrate the advantages and computational efficiency of the proposed algorithms over some existing results.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49231877","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}
. The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all n -vertex k -uniform hypertrees, we determine the k -uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all n -vertex k -uniform unicyclic hypergraphs, we obtain the k -uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the k -uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.
{"title":"Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs","authors":"Xiangxiang Liu, Ligong Wang","doi":"10.11650/tjm/220604","DOIUrl":"https://doi.org/10.11650/tjm/220604","url":null,"abstract":". The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all n -vertex k -uniform hypertrees, we determine the k -uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all n -vertex k -uniform unicyclic hypergraphs, we obtain the k -uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the k -uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43552524","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":"On Relaxed Greedy Randomized Iterative Methods for the Solution of Factorized Linear Systems","authors":"Shimin Liu, Y. Liu","doi":"10.11650/tjm/220305","DOIUrl":"https://doi.org/10.11650/tjm/220305","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64993722","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}
We prove Sobolev-type inequalities for modified Riesz potentials of functions in Morrey spaces of an integral form over non-doubling metric measure spaces. Our results are new even for the doubling metric measure setting. In particular, our results extend the previous results in Morrey spaces of an integral form in the Euclidean case.
{"title":"On Sobolev-type Inequalities on Morrey Spaces of an Integral Form","authors":"T. Ohno, T. Shimomura","doi":"10.11650/tjm/220203","DOIUrl":"https://doi.org/10.11650/tjm/220203","url":null,"abstract":"We prove Sobolev-type inequalities for modified Riesz potentials of functions in Morrey spaces of an integral form over non-doubling metric measure spaces. Our results are new even for the doubling metric measure setting. In particular, our results extend the previous results in Morrey spaces of an integral form in the Euclidean case.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44433721","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":"The $A_{alpha}$-spectral Radius of Bicyclic Graphs with Given Degree Sequences","authors":"Fei Wen, Mengyue Yuan, Wei Wang","doi":"10.11650/tjm/220906","DOIUrl":"https://doi.org/10.11650/tjm/220906","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44893824","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}
. In this paper, we investigate the L 2 boundedness of Fourier integral operator T φ,a with rough symbol a ∈ L ∞ S mρ and rough phase φ ∈ L ∞ Φ 2 which satisfies (cid:12)(cid:12) { x : |∇ ξ φ ( x, ξ ) − y | ≤ r } (cid:12)(cid:12) ≤ C ( r n − 1 + r n ) for any ξ, y ∈ R n and r > 0. We obtain that T φ,a is bounded on L 2 if m < ρ ( n − 1) / 2 − n/ 2 when 0 ≤ ρ ≤ 1 / 2 or m < − ( n + 1) / 4 when 1 / 2 ≤ ρ ≤ 1. When ρ = 0 or n = 1, the condition of m is sharp. Moreover, the maximal wave operator is a special class of T φ,a which is studied in this paper. Thus, our main theorem substantially extends and improves some known results about the maximal wave operator.
． 在这个L 2 boundedness》,这篇文章我们investigate傅立叶集成运营商Tφ和rough符号a∈a, L∞smρ和野蛮时期φ∈L∞Φ2萨蒂哪种fi冰(cid 12: 12) (cid) {x: |∇ξφ(x, yξ)−|≤r} (cid 12: 12) (cid)≤r C (n−1 + r∈r y n)为任何ξ,n和r > 0。我们得到那个φT,如果a是bounded on L 2 m <ρ(n−1)/ 2−n / 2当0≤ρ≤1 - 2或m <−(n + 1) / 4当1 / 2≤ρ≤1。当ρ= 0或n = 1, m是夏普之雾。而且,最大限度的浪潮是运营商a T特别届φ,哪种是studied in this paper)。因此，我们主要的物质扩展和一些最著名的结果关于最高浪潮运营商。
{"title":"Global $L^{2}$-boundedness of a New Class of Rough Fourier Integral Operators","authors":"Jiawei Dai, Qiang Huang","doi":"10.11650/tjm/220403","DOIUrl":"https://doi.org/10.11650/tjm/220403","url":null,"abstract":". In this paper, we investigate the L 2 boundedness of Fourier integral operator T φ,a with rough symbol a ∈ L ∞ S mρ and rough phase φ ∈ L ∞ Φ 2 which satisfies (cid:12)(cid:12) { x : |∇ ξ φ ( x, ξ ) − y | ≤ r } (cid:12)(cid:12) ≤ C ( r n − 1 + r n ) for any ξ, y ∈ R n and r > 0. We obtain that T φ,a is bounded on L 2 if m < ρ ( n − 1) / 2 − n/ 2 when 0 ≤ ρ ≤ 1 / 2 or m < − ( n + 1) / 4 when 1 / 2 ≤ ρ ≤ 1. When ρ = 0 or n = 1, the condition of m is sharp. Moreover, the maximal wave operator is a special class of T φ,a which is studied in this paper. Thus, our main theorem substantially extends and improves some known results about the maximal wave operator.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47526394","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":"Mixed Variational Inequality Interval-valued Problem: Theorems of Existence of Solutions","authors":"G. Ruiz-Garzón, R. Osuna-Gómez, J. Ruiz-Zapatero","doi":"10.11650/tjm/220503","DOIUrl":"https://doi.org/10.11650/tjm/220503","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45044305","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}
. This paper is concerned with studying the relaxed gradient-based iterative method based on tensor format to solve the Sylvester tensor equation. From the information given by the previous steps, we further develop a modified relaxed gradient-based iterative method which converges faster than the method above. Under some suitable conditions, we prove that the introduced methods are convergent to the unique solution for any initial tensor. At last, we provide some numerical examples to show that our methods perform much better than the GI algorithm proposed by Chen and Lu (Math. Probl. Eng. 2013) both in the number of iteration steps and the elapsed CPU time.
{"title":"On RGI Algorithms for Solving Sylvester Tensor Equations","authors":"Xin-Fang Zhang, Qingwen Wang","doi":"10.11650/tjm/220103","DOIUrl":"https://doi.org/10.11650/tjm/220103","url":null,"abstract":". This paper is concerned with studying the relaxed gradient-based iterative method based on tensor format to solve the Sylvester tensor equation. From the information given by the previous steps, we further develop a modified relaxed gradient-based iterative method which converges faster than the method above. Under some suitable conditions, we prove that the introduced methods are convergent to the unique solution for any initial tensor. At last, we provide some numerical examples to show that our methods perform much better than the GI algorithm proposed by Chen and Lu (Math. Probl. Eng. 2013) both in the number of iteration steps and the elapsed CPU time.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47201007","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}
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