Discrete & Continuous Dynamical Systems - S最新文献

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

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.

本文的目的是研究椭圆系统非平凡解的存在性，该解来自于一个新引入的数学问题，即Field-Road模型。具体地说，它是由不同维域中的耦合方程组和一些非经典类型的相互作用组成的。我们通过施加Dirichlet边界条件和无界设置来考虑截断问题。

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

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 begin{document}$ varphi $end{document} is designed in such a way to keep begin{document}$ varphi $end{document} in between the reference interval begin{document}$ (-1, 1) $end{document} 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.

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

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.

本文利用魏诺曼分解方法和李代数技术，证明了一个时变局部随机波动(SLV)模型可以简化为一个可以用热核求解的自治偏微分方程系统。然后，我们将传统的蒙特卡罗模拟结果与所述技术得到的显式解进行了比较。这种方法在文献中是新的，并且除了将非自治问题减少到自治问题之外，还允许更短的数值计算时间。

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

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.

本文的目的是研究肿瘤生长模型的最优控制问题。状态系统耦合了Allen-Cahn方程和反应扩散方程，模拟了肿瘤在营养供应下的进化。考虑通过细胞毒性药物消除癌细胞，并将细胞毒性药物的浓度表示为控制变量。

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

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.

本文讨论了带不确定性、时滞和外部干扰的区间2型模糊系统的动态滑模镇定问题。在控制设计过程中使用基于系统状态和控制输入向量的滑动曲面函数。通过定义一个增加系统状态和控制向量的新向量来描述滑模动力学。首先，证明了寻址滑模表面的可达性。其次，利用扩展耗散理论和非对称Lyapunov-Krasovskii泛函方法推导了系统稳定的充分条件和所提出的控制设计。与现有的一些滑模控制设计不同，本文提出的滑模控制设计不要求所有线性子系统的控制系数矩阵相同，降低了方法的保守性。最后，通过数值算例验证了所提设计方法的可行性和优越性。

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

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.

在Dirichlet边值条件下，研究了一类分数阶瞬时和非瞬时脉冲微分方程。利用Weierstrass定理给出了经典解的存在性。最后通过算例验证了所得结果的有效性。

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

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 begin{document}$ (1+t)^{-frac{1}{2}} $end{document} in begin{document}$ L^infty $end{document} norm.

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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

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.

本文的目的是分析一个氧气驱动肿瘤扩散和增殖的神经胶质瘤模型。我们证明了分析性问题的全局性，而且长期来看，这种疾病不会消失。此外，肿瘤的动态变化增加了氧含量。

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

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.

研究了具有多状态和输入时滞的高阶离散线性系统的极点配置问题。当状态延迟数大于或等于输入延迟数时，提出了一种有效的基于增强技术的预测反馈控制器，并给出了反馈增益的设计过程。此外，还证明了极点分配问题当且仅当线性矩阵方程的解使得矩阵非奇异时是可解的。当状态延迟数小于输入延迟数时，首先将原系统转化为无延迟系统，保持系统的可控性不变，然后建立相应的具有可设计反馈增益的控制器。为了描述所有的反馈增益，引入了一种可以提供全自由度的因数分解方法。数值算例说明了所提方法的有效性。

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

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 C¹ and C^{k, α} domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary.

As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.

研究了一类二阶抛物型线性方程在运动区域上解的边界行为。我们的主要结果是在C1和Ck， α域上的一个高阶边界Harnack不等式，假设两个解的商在域的边界上消失与边界一样光滑。在此基础上，给出了抛物型障碍问题中自由边界高阶正则性的一个新的证明。

引用次数: 8