European Journal of Applied Mathematics最新文献

{"title":"Optimal transport through a toll station","authors":"Arthur Stephanovitch, Anqi Dong, Tryphon T. Georgiou","doi":"10.1017/s0956792524000317","DOIUrl":"https://doi.org/10.1017/s0956792524000317","url":null,"abstract":"We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions, we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"214 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259868","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}

{"title":"Stabilization in a chemotaxis system modelling T-cell dynamics with simultaneous production and consumption of signals","authors":"Youshan Tao, Michael Winkler","doi":"10.1017/s0956792524000299","DOIUrl":"https://doi.org/10.1017/s0956792524000299","url":null,"abstract":"In a smoothly bounded domain <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline1.png\"/> <jats:tex-math> $Omega subset mathbb{R}^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline2.png\"/> <jats:tex-math> $nge 1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, this manuscript considers the homogeneous Neumann boundary problem for the chemotaxis system<jats:disp-formula> <jats:alternatives> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" position=\"float\" xlink:href=\"S0956792524000299_eqnU1.png\"/> <jats:tex-math> begin{eqnarray*} left { begin{array}{l} u_t = Delta u - nabla cdot (unabla v), [5pt] v_t = Delta v + u - alpha uv, end{array} right . end{eqnarray*} </jats:tex-math> </jats:alternatives> </jats:disp-formula>with parameter <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline3.png\"/> <jats:tex-math> $alpha gt 0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and with coincident production and uptake of attractants, as recently emphasized by Dallaston et al. as relevant for the understanding of T-cell dynamics. It is shown that there exists <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline4.png\"/> <jats:tex-math> $delta _star =delta _star (n)gt 0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> such that for any given <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline5.png\"/> <jats:tex-math> $alpha ge frac{1}{delta _star }$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and for any suitably regular initial data satisfying <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline6.png\"/> <jats:tex-math> $v(cdot, 0)le delta _star$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, this problem admits a unique classical solution that stabilizes to the constant equilibrium <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000299_inline7.png\"/> <jats:tex-math> $(frac{1}{|Omega |}int _Omega u(cdot, 0), , frac{1}{alpha })$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> in the large time limit.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"2 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259870","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}

{"title":"Exact recovery of community detection in k-community Gaussian mixture models","authors":"Zhongyang Li","doi":"10.1017/s0956792524000263","DOIUrl":"https://doi.org/10.1017/s0956792524000263","url":null,"abstract":"We study the community detection problem on a Gaussian mixture model, in which vertices are divided into <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000263_inline1.png\"/> <jats:tex-math> $kgeq 2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> distinct communities. The major difference in our model is that the intensities for Gaussian perturbations are different for different entries in the observation matrix, and we do not assume that every community has the same number of vertices. We explicitly find the necessary and sufficient conditions for the exact recovery of the maximum likelihood estimation, which can give a sharp phase transition for the exact recovery even though the Gaussian perturbations are not identically distributed; see Section 7. Applications include the community detection on hypergraphs.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"87 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259840","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}

{"title":"Travelling waves with continuous profile for hyperbolic Keller-Segel equation","authors":"Quentin Griette, Pierre Magal, Min Zhao","doi":"10.1017/s0956792524000305","DOIUrl":"https://doi.org/10.1017/s0956792524000305","url":null,"abstract":"This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion. We assume that cells try to avoid crowded areas and prefer locally empty spaces far away from the carrying capacity. Here, our main goal is to prove the existence of travelling waves with continuous profiles. This article complements our previous results about sharp travelling waves. We conclude the paper with numerical simulations of the PDE problem, illustrating such a result. An application to wound healing also illustrates the importance of travelling waves with a continuous and discontinuous profile.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"87 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259871","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}

{"title":"Local geometric properties of conductive transmission eigenfunctions and applications","authors":"Huaian Diao, Xiaoxu Fei, Hongyu Liu","doi":"10.1017/s0956792524000287","DOIUrl":"https://doi.org/10.1017/s0956792524000287","url":null,"abstract":"The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000287_inline1.png\"/> <jats:tex-math> $mathbb{R}^n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000287_inline2.png\"/> <jats:tex-math> $n=2,3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [26] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [26] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [26] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"31 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259864","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}

{"title":"Non-linear biphasic mixture model: Existence and uniqueness results","authors":"Meraj Alam, Adrian Muntean, Raja Sekhar G P","doi":"10.1017/s0956792524000251","DOIUrl":"https://doi.org/10.1017/s0956792524000251","url":null,"abstract":"This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumour. The classical mixture theory is adopted for mass and momentum balance equations for a two-phase system. A main contribution of this study is we treat the physiological transport parameter (i.e., hydraulic resistivity) as anisotropic and heterogeneous, thus the governing system is strongly coupled and non-linear. We derived a weak formulation and then formulated the equivalent fixed-point problem. This enabled us to use the Galerkin method, and the classical results on monotone operators combined with the well-known Schauder and Banach fixed-point theorems to prove the existence and uniqueness of results.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"29 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259865","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}

{"title":"Maintenance of steady-state mRNA levels by a microRNA-based feed forward loop in the presence of stochastic gene expression noise","authors":"Iryna Zabaikina, Pavol Bokes","doi":"10.1017/s095679252400024x","DOIUrl":"https://doi.org/10.1017/s095679252400024x","url":null,"abstract":"<p>All vital functions of living cells rely on the production of various functional molecules through gene expression. The production periods are burst-like and stochastic due to the discrete nature of biochemical reactions. In certain contexts, the concentrations of RNA or protein require regulation to maintain a fine internal balance within the cell. Here we consider a motif of two types of RNA molecules – mRNA and an antagonistic microRNA – which are encoded by a shared coding sequence and form a feed forward loop (FFL). This control mechanism is shown to be perfectly adapting in the deterministic context. We demonstrate that the adaptation (of the mean value) becomes imperfect if production occurs in random bursts. The FFL nevertheless outperforms the benchmark feedback loop in terms of counterbalancing variations in the signal. Methodologically, we adapt a hybrid stochastic model, which has widely been used to model a single regulatory molecule, to the current case of a motif involving two species; the use of the Laplace transform thereby circumvents the problem of moment closure that arises owing to the mRNA–microRNA interaction. We expect that the approach can be applicable to other systems with nonlinear kinetics.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"56 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168459","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}

{"title":"Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow","authors":"Tim Laux, Kerrek Stinson, Clemens Ullrich","doi":"10.1017/s0956792524000226","DOIUrl":"https://doi.org/10.1017/s0956792524000226","url":null,"abstract":"The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak–strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"88 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062608","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}

{"title":"Sufficiency of -cyclical monotonicity in a class of multi-marginal optimal transport problems","authors":"Luigi De Pascale, Anna Kausamo","doi":"10.1017/s0956792524000202","DOIUrl":"https://doi.org/10.1017/s0956792524000202","url":null,"abstract":"<p><span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240513153132896-0623:S0956792524000202:S0956792524000202_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$c$</span></span></img></span></span>-cyclical monotonicity is the most important optimality condition for an optimal transport plan. While the proof of necessity is relatively easy, the proof of sufficiency is often more difficult or even elusive. We present here a new approach, and we show how known results are derived in this new framework and how this approach allows to prove sufficiency in situations previously not treatable.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"66 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140933521","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}

{"title":"Unified framework for the separation property in binary phase-segregation processes with singular entropy densities","authors":"Ciprian G. Gal, Andrea Poiatti","doi":"10.1017/s0956792524000196","DOIUrl":"https://doi.org/10.1017/s0956792524000196","url":null,"abstract":"This paper investigates the separation property in binary phase-segregation processes modelled by Cahn-Hilliard type equations with constant mobility, singular entropy densities and different particle interactions. Under general assumptions on the entropy potential, we prove the strict separation property in both two and three-space dimensions. Namely, in 2D, we notably extend the minimal assumptions on the potential adopted so far in the literature, by only requiring a mild growth condition of its first derivative near the singular points <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000196_inline1.png\"/> <jats:tex-math> $pm 1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, without any pointwise additional assumption on its second derivative. For all cases, we provide a compact proof using De Giorgi’s iterations. In 3D, we also extend the validity of the asymptotic strict separation property to the case of fractional Cahn-Hilliard equation, as well as show the validity of the separation when the initial datum is close to an ‘energy minimizer’. Our framework offers insights into statistical factors like particle interactions, entropy choices and correlations governing separation, with broad applicability.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"60 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140933518","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}