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Dynamics for a Charge Transfer Model with Cross-Diffusion: Turing Instability of Periodic Solutions 具有交叉扩散的电荷转移模型的动力学：周期解的图灵不稳定性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-07-01 DOI: 10.1007/s10440-024-00666-x
Gaihui Guo, Jing You, Xinhuan Du, Yanling Li
{"title":"Dynamics for a Charge Transfer Model with Cross-Diffusion: Turing Instability of Periodic Solutions","authors":"Gaihui Guo,&nbsp;Jing You,&nbsp;Xinhuan Du,&nbsp;Yanling Li","doi":"10.1007/s10440-024-00666-x","DOIUrl":"10.1007/s10440-024-00666-x","url":null,"abstract":"<div><p>This paper is devoted to a charge transfer model with cross-diffusion under Neumann boundary conditions. We investigate how the cross-diffusion could destabilize the stable periodic solutions bifurcating from the unique positive equilibrium point. By the implicit function theorem and Floquet theory, we obtain some conditions on the self-diffusion and cross-diffusion coefficients under which the stable periodic solutions can become unstable. New irregular Turing patterns then generate by the destabilization of stable spatially homogeneous periodic solutions. We also present some numerical simulations to further support the results of theoretical analysis.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546478","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}
引用次数: 0
A New Parallel Algorithm for Solving a Class of Variational Inequalities 求解一类变分不等式的新并行算法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-06-19 DOI: 10.1007/s10440-024-00665-y
Nguyen Song Ha, Truong Minh Tuyen, Phan Thi Van Huyen
{"title":"A New Parallel Algorithm for Solving a Class of Variational Inequalities","authors":"Nguyen Song Ha,&nbsp;Truong Minh Tuyen,&nbsp;Phan Thi Van Huyen","doi":"10.1007/s10440-024-00665-y","DOIUrl":"10.1007/s10440-024-00665-y","url":null,"abstract":"<div><p>In this paper, we study the variational inequality over the solution set of the split common solution problem with multiple output sets for monotone operator equations in real Hilbert spaces. We propose a new approach for solving this problem without depending on the norm of the transfer mappings. Some of its applications for solving the variational inequality over the solution set of the split common fixed point problem with multiple output sets and related problems are also mentioned. Finally, we give numerical examples to illustrate the performance of the proposed algorithm and compare it with several existing previous algorithms.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546479","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}
引用次数: 0
Tumor Growth with a Necrotic Core as an Obstacle Problem in Pressure 带坏死核心的肿瘤生长是压力的一个障碍问题
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-06-07 DOI: 10.1007/s10440-024-00664-z
Xu’an Dou, Chengfeng Shen, Zhennan Zhou
{"title":"Tumor Growth with a Necrotic Core as an Obstacle Problem in Pressure","authors":"Xu’an Dou,&nbsp;Chengfeng Shen,&nbsp;Zhennan Zhou","doi":"10.1007/s10440-024-00664-z","DOIUrl":"10.1007/s10440-024-00664-z","url":null,"abstract":"<div><p>Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain <span>(Omega (t))</span>, and the coincidence set <span>(Lambda (t))</span> captures the emerging necrotic core. We contribute to the analytical characterization of the solution structure in the following two aspects. By deriving a semi-analytical solution and studying its dynamical behavior, we obtain quantitative transitional properties of the solution separating phases in the development of necrotic cores and establish its long time limit with the traveling wave solutions. Also, we prove the existence of traveling wave solutions incorporating non-zero outer densities outside the tumor bulk, provided that the size of the outer density is below a threshold.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546480","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}
引用次数: 0
Optimal Control for Biphasic Chemotaxis Model of Tumour Growth Under Chemotherapy 化疗条件下肿瘤生长的双相趋化模型的优化控制
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-06-05 DOI: 10.1007/s10440-024-00662-1
Sweta Sinha, Paramjeet Singh
{"title":"Optimal Control for Biphasic Chemotaxis Model of Tumour Growth Under Chemotherapy","authors":"Sweta Sinha,&nbsp;Paramjeet Singh","doi":"10.1007/s10440-024-00662-1","DOIUrl":"10.1007/s10440-024-00662-1","url":null,"abstract":"<div><p>Tumour growth is a complex process influenced by various factors, including cell proliferation, migration, and chemotaxis. In this study, a biphasic chemotaxis model for tumour growth is considered, and the effect of chemotherapy on the growth process is investigated. We use optimal control theory to derive the optimized treatment strategy that minimises the tumour size while minimising the toxicity associated with chemotherapy. Moreover, the existence, uniqueness, and strong solution estimates for the biphasic chemotaxis model subsystem in one dimension are derived. These results are achieved through semigroup theory and the truncation method. In addition, the research provides evidence of the existence of an optimal pair through the utilization of the minimising sequence technique. It also demonstrates the differentiability of the mapping from control variable to state variable and establishes the first-order necessary optimality condition. Lastly, a sequence of numerical simulations are presented to showcase the impact of chemotherapy and the influence of parameters in restraining tumour growth when applied in an optimized manner. Our results show that optimal control can provide a more effective and personalised treatment for cancer patients, and the approach can be extended to other tumour growth models.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00662-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well Posedness and Exponential Stability of a Porous Elastic System Free of Second Spectrum 无二次谱多孔弹性系统的良好假设性和指数稳定性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-06-03 DOI: 10.1007/s10440-024-00661-2
Afaf Ahmima, Abdelfeteh Fareh, Salim A. Messaoudi
{"title":"Well Posedness and Exponential Stability of a Porous Elastic System Free of Second Spectrum","authors":"Afaf Ahmima,&nbsp;Abdelfeteh Fareh,&nbsp;Salim A. Messaoudi","doi":"10.1007/s10440-024-00661-2","DOIUrl":"10.1007/s10440-024-00661-2","url":null,"abstract":"<div><p>This work focusses on the well–posedness and the exponential stability of a simplified porous elastic system. By omitting the second time derivative term of the function <span>(varphi )</span> in the porous elastic system, we make the system free of the damaging consequences of the second spectrum. We consider an elastic dissipation and prove the well–posedness by the use of Hille–Yosida therorem and some arguments of elliptic equations. Next, we use the multiplier method and establish an exponential decay result without any restriction on coefficients of the system.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253213","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}
引用次数: 0
Asymptotic Expansion of the Solutions to a Regularized Boussinesq System (Theory and Numerics) 正则化布森斯克系统解的渐近展开（理论与数值学）
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-06-03 DOI: 10.1007/s10440-024-00660-3
Ahmad Safa, Hervé Le Meur, Jean-Paul Chehab, Raafat Talhouk
{"title":"Asymptotic Expansion of the Solutions to a Regularized Boussinesq System (Theory and Numerics)","authors":"Ahmad Safa,&nbsp;Hervé Le Meur,&nbsp;Jean-Paul Chehab,&nbsp;Raafat Talhouk","doi":"10.1007/s10440-024-00660-3","DOIUrl":"10.1007/s10440-024-00660-3","url":null,"abstract":"<div><p>We consider the propagation of surface water waves described by the Boussinesq system. Following (Molinet et al. in Nonlinearity 34:744–775, 2021), we introduce a regularized Boussinesq system obtained by adding a non-local pseudo-differential operator define by <span>(widehat{g_{lambda }[zeta ]}=|k|^{lambda }hat{zeta }_{k})</span> with <span>(lambda in ]0,2])</span>. In this paper, we display a twofold approach: first, we study theoretically the existence of an asymptotic expansion for the solution to the Cauchy problem associated to this regularized Boussinesq system with respect to the regularizing parameter <span>(epsilon )</span>. Then, we compute numerically the function coefficients of the expansion (in <span>(epsilon )</span>) and verify numerically the validity of this expansion up to order 2. We also check the numerical <span>(L^{2})</span> stability of the numerical algorithm.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00660-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatio-Temporal Steady-State Analysis in a Prey-Predator Model with Saturated Hunting Cooperation and Chemotaxis 具有饱和狩猎合作和趋化作用的猎物-食肉动物模型的时空稳态分析
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-23 DOI: 10.1007/s10440-024-00658-x
Renji Han, Subrata Dey, Jicai Huang, Malay Banerjee
{"title":"Spatio-Temporal Steady-State Analysis in a Prey-Predator Model with Saturated Hunting Cooperation and Chemotaxis","authors":"Renji Han,&nbsp;Subrata Dey,&nbsp;Jicai Huang,&nbsp;Malay Banerjee","doi":"10.1007/s10440-024-00658-x","DOIUrl":"10.1007/s10440-024-00658-x","url":null,"abstract":"<div><p>In this paper, we propose a diffusive prey-predator model with saturated hunting cooperation and predator-taxis. We first establish the global classical solvability and boundedness, and provide some sufficient conditions to assure the existence of a unique positive homogeneous steady state and the global uniform asymptotic stability of the predator-free homogeneous steady state. Secondly, we study the pattern formation mechanism and reveal that pattern formation is driven by the joint effect of predator-taxis, hunting cooperation, and slow diffusivity of predators. Moreover, we find that a strong predator-taxis can annihilate the spatiotemporal patterns, but a weak predator-taxis supports the pattern formation when diffusion-driven instability is present in the model without predator-taxis. However, if diffusion-driven instability is absent, predator-taxis cannot destabilize the unique positive spatially homogeneous steady state. Additionally, we highlight that spatially heterogeneous steady states do not exist when the diffusion coefficient ratio of predators to prey is sufficiently large under specific parametric conditions. To explore the various types of spatially heterogeneous steady states, we derive amplitude equations based on the weakly nonlinear analysis theory. Finally, numerical simulations, including the hexagonal pattern, stripe pattern, a mixed pattern combining hexagons and stripes, and the square pattern, are presented to illustrate the theoretical results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141105605","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}
引用次数: 0
Error Bounds for Linear Complementarity Problems of Nekrasov and Generalized Nekrasov Matrices 涅克拉索夫矩阵和广义涅克拉索夫矩阵线性互补问题的误差界限
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-22 DOI: 10.1007/s10440-024-00659-w
Shiyun Wang, Dan Liu, Wanfu Tian, Zhen-Hua Lyu
{"title":"Error Bounds for Linear Complementarity Problems of Nekrasov and Generalized Nekrasov Matrices","authors":"Shiyun Wang,&nbsp;Dan Liu,&nbsp;Wanfu Tian,&nbsp;Zhen-Hua Lyu","doi":"10.1007/s10440-024-00659-w","DOIUrl":"10.1007/s10440-024-00659-w","url":null,"abstract":"<div><p>We first propose a new error bound for the linear complementarity problems when the involved matrices are generalized Nekrasov matrices, which generalizes the recent result obtained by Li et al. (Numer. Algorithms 74:997–1009, 2017). Then we present two new error bounds for the linear complementarity problems when the involved matrices are Nekrasov matrices. Numerical examples are given to illustrate the effectiveness of the proposed results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141110752","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}
引用次数: 0
A Mathematical Model for Assessing How Obesity-Related Factors Aggravate Diabetes 评估肥胖相关因素如何加重糖尿病的数学模型
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-16 DOI: 10.1007/s10440-024-00652-3
Ani Jain, Parimita Roy
{"title":"A Mathematical Model for Assessing How Obesity-Related Factors Aggravate Diabetes","authors":"Ani Jain,&nbsp;Parimita Roy","doi":"10.1007/s10440-024-00652-3","DOIUrl":"10.1007/s10440-024-00652-3","url":null,"abstract":"<div><p>Obesity-related factors have been associated with beta cell dysfunction, potentially leading to Type 2 diabetes. To address this issue, we developed a comprehensive obesity-based diabetes model incorporating fat cells, glucose, insulin, and beta cells. We established the model’s global existence, non-negativity, and boundedness. Additionally, we introduced a delay to examine the effects of impaired insulin production resulting from beta-cell dysfunction. Bifurcation analyses were conducted for delay and non-delay models, exploring the model’s dynamic transitions through backward and forward Hopf bifurcations. Utilizing the maximal Pontryagin principle, we formulated and evaluated an optimal control problem to mitigate diabetic complications by reducing the prevalence of overweight individuals and halting disease progression. Comparative graphical outputs were generated to demonstrate the beneficial effects of glucose-regulating medication and regular exercise in managing diabetes.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140969497","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}
引用次数: 0
Boundedness and Finite-Time Blow-up in a Chemotaxis System with Flux Limitation and Logistic Source 具有流量限制和逻辑源的趋化系统中的有界性和有限时间爆炸
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-16 DOI: 10.1007/s10440-024-00653-2
Shohei Kohatsu
{"title":"Boundedness and Finite-Time Blow-up in a Chemotaxis System with Flux Limitation and Logistic Source","authors":"Shohei Kohatsu","doi":"10.1007/s10440-024-00653-2","DOIUrl":"10.1007/s10440-024-00653-2","url":null,"abstract":"<div><p>The chemotaxis system </p><div><div><span> $$begin{aligned} textstylebegin{cases} u_{t}=Delta u - chi nabla cdot (u|nabla v|^{p-2}nabla v) + lambda u - mu u^{kappa }, 0=Delta v + u - h(u,v) end{cases}displaystyle end{aligned}$$ </span></div><div>\u0000 (∗)\u0000 </div></div><p> is considered in a smoothly bounded domain <span>(Omega subset mathbb{R}^{n})</span> (<span>(n in mathbb{N})</span>), where <span>(chi &gt; 0)</span>, <span>(p &gt; 1)</span>, <span>(lambda ge 0)</span>, <span>(mu &gt; 0)</span>, <span>(kappa &gt; 1)</span>, and <span>(h = v)</span> or <span>(h = frac{1}{|Omega |} int _{Omega } u)</span>. It is firstly proved that if <span>(n = 1)</span> and <span>(p &gt; 1)</span> is arbitrary, or <span>(n ge 2)</span> and <span>(p in (1, frac{n}{n-1}))</span>, then for all continuous initial data a corresponding no-flux type initial-boundary value problem for <span>((ast ))</span> admits a globally defined and bounded weak solution. Secondly, it is shown that if <span>(n ge 2)</span>, <span>(Omega = B_{R}(0) subset mathbb{R}^{n})</span> is a ball with some <span>(R &gt; 0)</span>, <span>(p &gt; frac{n}{n-1})</span> and <span>(kappa &gt; 1)</span> is small enough, then one can find a nonnegative radially symmetric function <span>(u_{0})</span> and a weak solution of <span>((ast ))</span> with initial datum <span>(u_{0})</span> which blows up in finite time.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971823","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}
引用次数: 0
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