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On some model problem for the propagation of interacting species in a special environment 特殊环境下相互作用物种繁殖的一些模型问题
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-05-12 DOI: 10.3934/dcds.2020401
M. Chipot, Mingmin Zhang
{"title":"On some model problem for the propagation of interacting species in a special environment","authors":"M. Chipot, Mingmin Zhang","doi":"10.3934/dcds.2020401","DOIUrl":"https://doi.org/10.3934/dcds.2020401","url":null,"abstract":"The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in domains of different dimensions together with some interaction of non classical type. We consider a truncated problem by imposing Dirichlet boundary conditions and an unbounded setting as well.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82569031","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}
引用次数: 2
On the Cahn-Hilliard-Darcy system with mass source and strongly separating potential 具有质量源和强分离势的Cahn-Hilliard-Darcy体系
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-02-23 DOI: 10.3934/dcdss.2022008
G. Schimperna
{"title":"On the Cahn-Hilliard-Darcy system with mass source and strongly separating potential","authors":"G. Schimperna","doi":"10.3934/dcdss.2022008","DOIUrl":"https://doi.org/10.3934/dcdss.2022008","url":null,"abstract":"<p style='text-indent:20px;'>We study an evolutionary system of Cahn-Hilliard-Darcy type including mass source and transport effects. The system may arise in a number of physical situations related to phase separation phenomena with convection, with the main and most specific application being related to tumoral processes, where the variations of the mass may correspond to growth, or shrinking, of the tumor. We prove existence of weak solutions in the case when the configuration potential for the order parameter <inline-formula><tex-math id=\"M1\">begin{document}$ varphi $end{document}</tex-math></inline-formula> is designed in such a way to keep <inline-formula><tex-math id=\"M2\">begin{document}$ varphi $end{document}</tex-math></inline-formula> in between the reference interval <inline-formula><tex-math id=\"M3\">begin{document}$ (-1, 1) $end{document}</tex-math></inline-formula> despite the occurrence of mass source effects. Moreover, in the two-dimensional case, we obtain existence and uniqueness of strong (i.e., more regular) solutions.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77756879","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}
引用次数: 4
Stochastic local volatility models and the Wei-Norman factorization method 随机局部波动模型和魏-诺曼分解法
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-27 DOI: 10.3934/dcdss.2022026
J. Guerrero, G. Orlando
{"title":"Stochastic local volatility models and the Wei-Norman factorization method","authors":"J. Guerrero, G. Orlando","doi":"10.3934/dcdss.2022026","DOIUrl":"https://doi.org/10.3934/dcdss.2022026","url":null,"abstract":"In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of autonomous PDEs that can be solved using the heat kernel, by means of the Wei-Norman factorization method and Lie algebraic techniques. Then, we compare the results of traditional Monte Carlo simulations with the explicit solutions obtained by said techniques. This approach is new in the literature and, in addition to reducing a non-autonomous problem into an autonomous one, allows for shorter time in numerical computations.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81192777","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}
引用次数: 1
Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs 细胞毒性药物对肿瘤生长的Allen-Cahn模型最优控制
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcdss.2022003
Hawraa Alsayed, Hussein Fakih, A. Miranville, A. Wehbe
{"title":"Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs","authors":"Hawraa Alsayed, Hussein Fakih, A. Miranville, A. Wehbe","doi":"10.3934/dcdss.2022003","DOIUrl":"https://doi.org/10.3934/dcdss.2022003","url":null,"abstract":"Our aim in this paper is to study an optimal control problem for a tumor growth model. The state system couples an Allen-Cahn equation and a reaction diffusion equation that models the evolution of tumor in the presence of nutrient supply. Elimination of cancer cells via cytotoxic drug is considered and the concentration of the cytotoxic drug is represented as a control variable.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86064975","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}
引用次数: 3
Robust dynamic sliding mode control design for interval type-2 fuzzy systems 区间2型模糊系统的鲁棒动态滑模控制设计
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcdss.2022014
R. Kavikumar, B. Kaviarasan, Yonggwon Lee, O. Kwon, R. Sakthivel, Seong-Gon Choi
{"title":"Robust dynamic sliding mode control design for interval type-2 fuzzy systems","authors":"R. Kavikumar, B. Kaviarasan, Yonggwon Lee, O. Kwon, R. Sakthivel, Seong-Gon Choi","doi":"10.3934/dcdss.2022014","DOIUrl":"https://doi.org/10.3934/dcdss.2022014","url":null,"abstract":"This paper discusses the problem of stabilization of interval type-2 fuzzy systems with uncertainties, time delay and external disturbance using a dynamic sliding mode controller. The sliding surface function, which is based on both the system's state and control input vectors, is used during the control design process. The sliding mode dynamics are presented by defining a new vector that augments the system state and control vectors. First, the reachability of the addressed sliding mode surface is demonstrated. Second, the required sufficient conditions for the system's stability and the proposed control design are derived by using extended dissipative theory and an asymmetric Lyapunov-Krasovskii functional approach. Unlike some existing sliding mode control designs, the one proposed in this paper does not require the control coefficient matrices of all linear subsystems to be the same, reducing the method's conservatism. Finally, numerical examples are provided to demonstrate the viability and superiority of the proposed design method.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82723218","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}
引用次数: 3
Existence of solutions for fractional instantaneous and non-instantaneous impulsive differential equations with perturbation and Dirichlet boundary value 具有微扰和Dirichlet边值的分数阶瞬时和非瞬时脉冲微分方程解的存在性
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcdss.2022005
Yinuo Wang, Chuandong Li, Hongjuan Wu, Hao Deng
{"title":"Existence of solutions for fractional instantaneous and non-instantaneous impulsive differential equations with perturbation and Dirichlet boundary value","authors":"Yinuo Wang, Chuandong Li, Hongjuan Wu, Hao Deng","doi":"10.3934/dcdss.2022005","DOIUrl":"https://doi.org/10.3934/dcdss.2022005","url":null,"abstract":"A class of fractional instantaneous and non-instantaneous impulsive differential equations under Dirichlet boundary value conditions with perturbation is considered here. The existence of classical solutions is presented by using the Weierstrass theorem. An example is given to verify the validity of the obtained results.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80598283","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}
引用次数: 3
Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space 半空间中一维可压缩naver - stokes方程解的点态估计
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcds.2021205
Hai-liang Li, H. Tang, Haitao Wang
{"title":"Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space","authors":"Hai-liang Li, H. Tang, Haitao Wang","doi":"10.3934/dcds.2021205","DOIUrl":"https://doi.org/10.3934/dcds.2021205","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we study the global existence and pointwise behavior of classical solution to one dimensional isentropic Navier-Stokes equations with mixed type boundary condition in half space. Based on classical energy method for half space problem, the global existence of classical solution is established firstly. Through analyzing the quantitative relationships of Green's function between Cauchy problem and initial boundary value problem, we observe that the leading part of Green's function for the initial boundary value problem is composed of three items: delta function, diffusive heat kernel, and reflected term from the boundary. Then applying Duhamel's principle yields the explicit expression of solution. With the help of accurate estimates for nonlinear wave coupling and the elliptic structure of velocity, the pointwise behavior of the solution is obtained under some appropriate assumptions on the initial data. Our results prove that the solution converges to the equilibrium state at the optimal decay rate <inline-formula><tex-math id=\"M1\">begin{document}$ (1+t)^{-frac{1}{2}} $end{document}</tex-math></inline-formula> in <inline-formula><tex-math id=\"M2\">begin{document}$ L^infty $end{document}</tex-math></inline-formula> norm.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86354896","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}
引用次数: 1
An oxygen driven proliferative-to-invasive transition of glioma cells: An analytical study 氧驱动胶质瘤细胞从增殖到侵袭的转变:一项分析研究
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcdss.2022002
S. Gatti
{"title":"An oxygen driven proliferative-to-invasive transition of glioma cells: An analytical study","authors":"S. Gatti","doi":"10.3934/dcdss.2022002","DOIUrl":"https://doi.org/10.3934/dcdss.2022002","url":null,"abstract":"<p style='text-indent:20px;'>Our aim in this paper is to analyze a model of glioma where oxygen drives cancer diffusion and proliferation. We prove the global well-posedness of the analytical problem and that, in the longtime, the illness does not disappear. Besides, the tumor dynamics increase the oxygen levels.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87428251","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}
引用次数: 2
On pole assignment of high-order discrete-time linear systems with multiple state and input delays 具有多状态和输入延迟的高阶离散线性系统的极点配置
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcdss.2022022
Li-Xian Zhang, Xuefei Yang
{"title":"On pole assignment of high-order discrete-time linear systems with multiple state and input delays","authors":"Li-Xian Zhang, Xuefei Yang","doi":"10.3934/dcdss.2022022","DOIUrl":"https://doi.org/10.3934/dcdss.2022022","url":null,"abstract":"This paper studies the problem of pole assignment for high-order discrete-time linear systems with multiple state and input delays. When the number of state delays is larger than or equal to that of input delays, an effective predictor feedback controller is proposed based on the augmented technique, and the design process for the feedback gain is also presented. In addition, it is proved that the pole assignment problem is solvable if and only if the solutions to a linear matrix equation are such that a matrix is nonsingular. When the number of state delays is smaller than that of input delays, the original system is first transformed into a delay-free system with keeping the system controllability invariant, and then, the corresponding controller with designable feedback gain is established. To characterize all of the feedback gains, a factorization approach is introduced which can provide full degree of freedom. Numerical examples are employed to illustrate the effectiveness of the proposed approaches.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77376277","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}
引用次数: 1
Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains C1和Ck， α域上的高阶抛物边界Harnack不等式
Discrete & Continuous Dynamical Systems - S Pub Date : 2022-01-01 DOI: 10.3934/dcds.2021207
Teo Kukuljan
{"title":"Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains","authors":"Teo Kukuljan","doi":"10.3934/dcds.2021207","DOIUrl":"https://doi.org/10.3934/dcds.2021207","url":null,"abstract":"<p style='text-indent:20px;'>We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in <i>C</i><sup>1</sup> and <i>C</i><sup><i>k</i>, <i>α</i></sup> domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary.</p><p style='text-indent:20px;'>As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77396449","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}
引用次数: 8
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