Applied Mathematics and Optimization最新文献_第8页

Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains 扩展域中准线性椭圆问题的多重正解

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-29 DOI: 10.1007/s00245-024-10155-0

Wulong Liu, Guowei Dai, Patrick Winkert, Shengda Zeng

引用次数: 0

Continuous-Time Mean Field Markov Decision Models 连续时间均值场马尔可夫决策模型

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-22 DOI: 10.1007/s00245-024-10154-1

Nicole Bäuerle, Sebastian Höfer

{"title":"Continuous-Time Mean Field Markov Decision Models","authors":"Nicole Bäuerle, Sebastian Höfer","doi":"10.1007/s00245-024-10154-1","DOIUrl":"10.1007/s00245-024-10154-1","url":null,"abstract":"<div>We consider a finite number of N statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on the state and action of the agent itself, but also on the states of the other agents as well as the chosen action. Interactions like this are typical for a wide range of models in e.g. biology, epidemics, finance, social science and queueing systems among others. The aim is to maximize the expected discounted reward of the system, i.e. the agents have to cooperate as a team. Computationally this is a difficult task when N is large. Thus, we consider the limit for (Nrightarrow infty .) In contrast to other papers we treat this problem from an MDP perspective. This has the advantage that we need less regularity assumptions in order to construct asymptotically optimal strategies than using viscosity solutions of HJB equations. The convergence rate is (1/sqrt{N}). We show how to apply our results using two examples: a machine replacement problem and a problem from epidemics. We also show that optimal feedback policies from the limiting problem are not necessarily asymptotically optimal.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10154-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Global Behavior in a Two-Species Chemotaxis-Competition System with Signal-Dependent Sensitivities and Nonlinear Productions 具有信号敏感性和非线性产物的双物种趋化竞争系统的全局行为

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-22 DOI: 10.1007/s00245-024-10137-2

Zhan Jiao, Irena Jadlovská, Tongxing Li

{"title":"Global Behavior in a Two-Species Chemotaxis-Competition System with Signal-Dependent Sensitivities and Nonlinear Productions","authors":"Zhan Jiao, Irena Jadlovská, Tongxing Li","doi":"10.1007/s00245-024-10137-2","DOIUrl":"10.1007/s00245-024-10137-2","url":null,"abstract":"<div>This article considers a two competitive biological species system involving signal-dependent motilities and sensitivities and nonlinear productions <div><div>$$begin{aligned} left{ begin{array}{l} begin{aligned} &{}u_t = nabla cdot big (D_1(v)nabla u-uS_1(v)nabla vbig )+mu _1u(1-u^{alpha _1}-a_1w),&{} xin Omega , t>0&{}, &{} v_t=Delta v-v+b_1w^{gamma _1}, &{} xin Omega , t>0&{}, &{}w_t = nabla cdot big (D_2(z)nabla w-wS_2(z)nabla zbig )+mu _2w(1-w^{alpha _2}-a_2u),&{} xin Omega , t>0&{}, &{} z_t=Delta z-z+b_2u^{gamma _2}, &{} xin Omega , t>0&{} end{aligned} end{array} right. end{aligned}$$</div></div>in a bounded and smooth domain (Omega subset mathbb R^2), where the parameters (mu _i, alpha _i, a_i, b_i, gamma _i) ((i=1,2)) are positive constants, and the functions (D_1(v),S_1(v),D_2(z),S_2(z)) fulfill the following hypotheses: (Diamond ) (D_i(psi ),S_i(psi )in C^2([0,infty ))), (D_i(psi ),S_i(psi )>0) for all (psi ge 0), (D_i^{prime }(psi )<0) and (underset{psi rightarrow infty }{lim } D_i(psi )=0); (Diamond ) (underset{psi rightarrow infty }{lim } frac{S_i(psi )}{D_i(psi )}) and (underset{psi rightarrow infty }{lim } frac{D^{prime }_i(psi )}{D_i(psi )}) exist. We first confirm the global boundedness of the classical solution provided that the additional conditions (2gamma _1le 1+alpha _2) and (2gamma _2le 1+alpha _1) hold. Moreover, by constructing several suitable Lyapunov functionals, it is demonstrated that the global solution exponentially or algebraically converges to the constant stationary solutions and the corresponding convergence rates are determined under some specific stress conditions.\u0000</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Entropic Approximation of (infty )-Optimal Transport Problems 最优传输问题的熵逼近

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-18 DOI: 10.1007/s00245-024-10136-3

Camilla Brizzi, Guillaume Carlier, Luigi De Pascale

引用次数: 0

Uniform Large Deviation Principle for the Solutions of Two-Dimensional Stochastic Navier–Stokes Equations in Vorticity Form 二维随机纳维-斯托克斯方程涡度形式解的均匀大偏差原理

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-17 DOI: 10.1007/s00245-024-10150-5

Ankit Kumar, Manil T. Mohan

{"title":"Uniform Large Deviation Principle for the Solutions of Two-Dimensional Stochastic Navier–Stokes Equations in Vorticity Form","authors":"Ankit Kumar, Manil T. Mohan","doi":"10.1007/s00245-024-10150-5","DOIUrl":"10.1007/s00245-024-10150-5","url":null,"abstract":"<div>The main objective of this paper is to demonstrate the uniform large deviation principle (UDLP) for the solutions of two-dimensional stochastic Navier–Stokes equations (SNSE) in the vorticity form when perturbed by two distinct types of noises. We first consider an infinite-dimensional additive noise that is white in time and colored in space and then consider a finite-dimensional Wiener process with linear growth coefficient. In order to obtain the ULDP for 2D SNSE in the vorticity form, where the noise is white in time and colored in space, we utilize the existence and uniqueness result from B. Ferrario et. al., Stochastic Process. Appl., 129 (2019), 1568–1604, and the uniform contraction principle. For the finite-dimensional multiplicative Wiener noise, we first prove the existence of a unique local mild solution to the vorticity equation using a truncation and fixed point arguments. We then establish the global existence of the truncated system by deriving a uniform energy estimate for the local mild solution. By applying stopping time arguments and a version of Skorokhod’s representation theorem, we conclude the global existence and uniqueness of a solution to our model. We employ the weak convergence approach to establish the ULDP for the law of the solutions in two distinct topologies. We prove ULDP in the ({{textrm{C}}([0,T];{textrm{L}}^p({mathbb {T}}^2))}) topology, for (p>2), taking into account the uniformity of the initial conditions contained in bounded subsets of ({{textrm{L}}^p({mathbb {T}}^2)}). Finally, in ({{textrm{C}}([0,T]times {mathbb {T}}^2)}) topology, the uniformity of initial conditions lying in bounded subsets of ({{textrm{C}}({mathbb {T}}^2)}) is considered.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Convexification Numerical Method for the Retrospective Problem of Mean Field Games 平均场博弈回溯问题的凸化数值法

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-14 DOI: 10.1007/s00245-024-10152-3

Michael V. Klibanov, Jingzhi Li, Zhipeng Yang

引用次数: 0

Correction to: Existence of Pseudo-Relative Sharp Minimizers in Set-Valued Optimization 更正：集值优化中伪相对锐最小化的存在性

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-14 DOI: 10.1007/s00245-024-10147-0

Tijani Amahroq, Abdessamad Oussarhan

引用次数: 0

On the Small-Mass Limit for Stationary Solutions of Stochastic Wave Equations with State Dependent Friction 论具有状态相关摩擦力的随机波方程静态解的小质量极限

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-14 DOI: 10.1007/s00245-024-10153-2

Sandra Cerrai, Mengzi Xie

引用次数: 0

Pontryagin’s Principle for Some Probabilistic Control Problems 某些概率控制问题的庞特里亚金原理

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-05 DOI: 10.1007/s00245-024-10151-4

Wim van Ackooij, René Henrion, Hasnaa Zidani

引用次数: 0

Infinite Horizon Mean-Field Linear Quadratic Optimal Control Problems with Jumps and the Related Hamiltonian Systems 带跳跃的无限地平线均场线性二次优化控制问题及相关哈密顿系统

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-04 DOI: 10.1007/s00245-024-10148-z

Qingmeng Wei, Yaqi Xu, Zhiyong Yu

引用次数: 0