Pub Date : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0041
Feng Dai null, Bin Liu
. This paper deals with the four-component Keller-Segel-Stokes model of coral fertilization in a bounded and smooth domain Ω ⊂ R 3 with zero-flux boundary for n , c , ρ and no-slip boundary for u , where m > 0, φ ∈ W 2, ∞ ( Ω ) , and S : ¯ Ω × [ 0, ∞ ) 2 → R 3 × 3 is given suffi-ciently smooth function such that | S ( x , n , c ) |≤ S 0 ( c )( n + 1 ) − α for all ( x , n , c ) ∈ ¯ Ω × [ 0, ∞ ) 2 with α ≥ 0 and some nondecreasing function S 0 : [ 0, ∞ ) 7→ [ 0, ∞ ) . It is shown that if m > 1 − α for 0 ≤ α ≤ 23 , or m ≥ 13 for α > 23 , then for any reasonably regular initial data, the corresponding initial-boundary value problem admits at least one globally bounded weak solution which stabilizes to the spatially homogeneous equilibrium ( n ∞ , ρ ∞ , ρ ∞ ,0 ) in an appropriate sense, where n ∞ : = 1 | Ω | (cid:8) R Ω n 0 − R Ω ρ 0 (cid:9) + and ρ ∞ : = 1 | Ω | (cid:8) R Ω ρ 0 − R Ω n 0 (cid:9) + . These results improve and extend previously known ones.
。摘要珊瑚受精的四分量Keller-Segel-Stokes模型在有界和平稳域Ω⊂R 3与零边界n, c,ρ和无滑动边界u, m > 0,φ∈W 2∞(Ω)和S:¯Ω×[0,∞)2→R 3×3给出其光滑函数,这样| S (x) n, c) |≤0 S (c) (n + 1)−α为所有(x, n, c)∈¯Ω×[0,∞)与α2≥0和一些不减少的功能年代0:[0,∞)7→[0,∞)。结果表明,如果m > 1−α为0≤α≤23日或m≥13α> 23日,然后对于任何合理规律的初始数据,相应的初边值问题承认至少一个全局有界弱解的稳定空间齐次平衡(n∞,ρ∞,ρ∞,0)在一个合适的意义上,其中n∞:= 1 |Ω| (cid: 8) 0Ωn−RΩρ0 (cid: 9) +和ρ∞:= 1 |Ω| (cid: 8) RΩρ0−RΩn 0 (cid: 9) +。这些结果改进并扩展了以前已知的结果。
{"title":"Boundedness and Asymptotic Behavior in a 3D Keller-Segel-Stokes System Modeling Coral Fertilization with Nonlinear Diffusion and Rotation","authors":"Feng Dai null, Bin Liu","doi":"10.4208/csiam-am.so-2021-0041","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0041","url":null,"abstract":". This paper deals with the four-component Keller-Segel-Stokes model of coral fertilization in a bounded and smooth domain Ω ⊂ R 3 with zero-flux boundary for n , c , ρ and no-slip boundary for u , where m > 0, φ ∈ W 2, ∞ ( Ω ) , and S : ¯ Ω × [ 0, ∞ ) 2 → R 3 × 3 is given suffi-ciently smooth function such that | S ( x , n , c ) |≤ S 0 ( c )( n + 1 ) − α for all ( x , n , c ) ∈ ¯ Ω × [ 0, ∞ ) 2 with α ≥ 0 and some nondecreasing function S 0 : [ 0, ∞ ) 7→ [ 0, ∞ ) . It is shown that if m > 1 − α for 0 ≤ α ≤ 23 , or m ≥ 13 for α > 23 , then for any reasonably regular initial data, the corresponding initial-boundary value problem admits at least one globally bounded weak solution which stabilizes to the spatially homogeneous equilibrium ( n ∞ , ρ ∞ , ρ ∞ ,0 ) in an appropriate sense, where n ∞ : = 1 | Ω | (cid:8) R Ω n 0 − R Ω ρ 0 (cid:9) + and ρ ∞ : = 1 | Ω | (cid:8) R Ω ρ 0 − R Ω n 0 (cid:9) + . These results improve and extend previously known ones.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48545260","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0001
Fangfang Xu, Yating Wang, Yanyan Li, Lu Liu null, Tonghua Tian
{"title":"Gradient Type Methods for Linear Hyperspectral Unmixing","authors":"Fangfang Xu, Yating Wang, Yanyan Li, Lu Liu null, Tonghua Tian","doi":"10.4208/csiam-am.so-2021-0001","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0001","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46986089","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2022-0001
Yongkun Li null, Xiaoli Huang
{"title":"Weyl Almost Periodic Solutions in Distribution of Clifford-Valued Stochastic High-Order Hopfield Neural Networks with Delays on Time Scales","authors":"Yongkun Li null, Xiaoli Huang","doi":"10.4208/csiam-am.so-2022-0001","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2022-0001","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43646268","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2020-0006
Jihong Wang, Z. Xu, Jiwei Zhang null, Yaoyu Zhang
{"title":"Implicit Bias in Understanding Deep Learning for Solving PDEs Beyond Ritz-Galerkin Method","authors":"Jihong Wang, Z. Xu, Jiwei Zhang null, Yaoyu Zhang","doi":"10.4208/csiam-am.so-2020-0006","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2020-0006","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46812325","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0036
Guanghua Ji, Zhen Xu null, Yuqi Yang
. In this paper, we develop a fully discrete scheme to solve the confined ternary blended polymers (TBP) model with four order parameters based on the stabilized-scalar auxiliary variable (S-SAV) approach in time and the Fourier spectral method in space. Then, theoretical analysis is given for the scheme based on the back-ward differentiation formula. The unconditional energy stability and mass conserva-tion are derived. Rigorous error analysis is carried out to show that the fully discrete scheme converges with order O ( τ 2 + h m ) in the sense of the L 2 norm, where τ is the time step, h is the spatial step, and m is the regularity of the exact solution. Finally, some numerical results are given to demonstrate the theoretical analysis. Moreover, the phase separation of two kinds of polymer particles, namely, Ashura and Janus core-shell particles, is presented to show the morphological structures.
{"title":"An Efficient and Unconditionally Energy Stable Fully Discrete Scheme for the Confined Ternary Blended Polymers Model","authors":"Guanghua Ji, Zhen Xu null, Yuqi Yang","doi":"10.4208/csiam-am.so-2021-0036","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0036","url":null,"abstract":". In this paper, we develop a fully discrete scheme to solve the confined ternary blended polymers (TBP) model with four order parameters based on the stabilized-scalar auxiliary variable (S-SAV) approach in time and the Fourier spectral method in space. Then, theoretical analysis is given for the scheme based on the back-ward differentiation formula. The unconditional energy stability and mass conserva-tion are derived. Rigorous error analysis is carried out to show that the fully discrete scheme converges with order O ( τ 2 + h m ) in the sense of the L 2 norm, where τ is the time step, h is the spatial step, and m is the regularity of the exact solution. Finally, some numerical results are given to demonstrate the theoretical analysis. Moreover, the phase separation of two kinds of polymer particles, namely, Ashura and Janus core-shell particles, is presented to show the morphological structures.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42577141","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0037
Wei Wang null, Ruofan Liu
. In this paper, we propose and develop a saturation value total variation (SV-TV) regularization model for simultaneously image denoising and luminance adjustment. The idea is to propose a variational approach containing an energy functional to adjust the luminance between image patches, and the noise of the image can be removed. In the proposed model, we establish the adjustment term based on the concept of structure, luminance, and contrast similarity, and we make use of the SV-TV regularization to remove the noise simultaneously. We present an efficient and effective algorithm with convergence guaranteed to solve the proposed minimization model. Experimental results are presented to show the effectiveness of the proposed model compared with existing methods.
{"title":"A Variational Model for Simultaneously Image Denoising and Luminance Adjustment","authors":"Wei Wang null, Ruofan Liu","doi":"10.4208/csiam-am.so-2021-0037","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0037","url":null,"abstract":". In this paper, we propose and develop a saturation value total variation (SV-TV) regularization model for simultaneously image denoising and luminance adjustment. The idea is to propose a variational approach containing an energy functional to adjust the luminance between image patches, and the noise of the image can be removed. In the proposed model, we establish the adjustment term based on the concept of structure, luminance, and contrast similarity, and we make use of the SV-TV regularization to remove the noise simultaneously. We present an efficient and effective algorithm with convergence guaranteed to solve the proposed minimization model. Experimental results are presented to show the effectiveness of the proposed model compared with existing methods.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48114496","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0005
Zhenzhen Lou, Jianfeng Wang null, Qiongxiang Huang
{"title":"On the Distance Cospectrality of Threshold Graphs","authors":"Zhenzhen Lou, Jianfeng Wang null, Qiongxiang Huang","doi":"10.4208/csiam-am.so-2021-0005","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0005","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44836697","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0033
Haicheng Liu, Bin Ge null, Ji-hong Shen
{"title":"Spatiotemporal Dynamics in a Generalized Diffusive Population System of Natural Pinus Koraiensis with Time Delay","authors":"Haicheng Liu, Bin Ge null, Ji-hong Shen","doi":"10.4208/csiam-am.so-2021-0033","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0033","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46443546","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 : 2022-06-01DOI: 10.4208/csiam-am.so-2021-0015
Jue Wang, Hongwei Ding null, Lei Zhang
{"title":"Numerical Research for the 2D Vorticity-Stream Function Formulation of the Navier-Stokes Equations and its application in Vortex Merging at High Reynolds Numbers","authors":"Jue Wang, Hongwei Ding null, Lei Zhang","doi":"10.4208/csiam-am.so-2021-0015","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0015","url":null,"abstract":"","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46245324","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}
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