Communications in Partial Differential Equations最新文献_第10页

A transmission problem with (p, q)-Laplacian 具有（p，q）-Laplacian算子的一个传输问题

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-06-14 DOI: 10.1080/03605302.2023.2175216

Maria Colombo, Sunghan Kim, H. Shahgholian

引用次数: 2

Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption 具有密度抑制运动和营养消耗的趋化系统的整体存在性、均匀有界性和稳定性

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-06-02 DOI: 10.1080/03605302.2021.2021422

Jie Jiang, P. Laurençot, Yanyan Zhang

引用次数: 12

L 2-type Lyapunov functions for hyperbolic scalar conservation laws 双曲标量守恒律的L2型李雅普诺夫函数

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-06-01 DOI: 10.1080/03605302.2021.1983597

D. Serre

引用次数: 0

On gradient estimates for heat kernels 热核的梯度估计

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-05-27 DOI: 10.1080/03605302.2020.1857398

Baptiste Devyver

引用次数: 0

Optimisation of the total population size for logistic diffusive equations: bang-bang property and fragmentation rate 逻辑扩散方程总种群规模的优化：bang-bang性质和碎片率

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-05-21 DOI: 10.1080/03605302.2021.2007533

Idriss Mazari, Grégoire Nadin, Y. Privat

{"title":"Optimisation of the total population size for logistic diffusive equations: bang-bang property and fragmentation rate","authors":"Idriss Mazari, Grégoire Nadin, Y. Privat","doi":"10.1080/03605302.2021.2007533","DOIUrl":"https://doi.org/10.1080/03605302.2021.2007533","url":null,"abstract":"Abstract In this article, we give an in-depth analysis of the problem of optimising the total population size for a standard logistic-diffusive model. This optimisation problem stems from the study of spatial ecology and amounts to the following question: assuming a species evolves in a domain, what is the best way to spread resources in order to ensure a maximal population size at equilibrium? In recent years, many authors contributed to this topic. We settle here the proof of two fundamental properties of optimisers: the bang-bang one, which had so far only been proved under several strong assumptions, and the other one is the fragmentation of maximisers. We prove the bang-bang property in all generality using a new spectral method. The technique introduced to demonstrate the bang-bang character of optimisers can be adapted and generalised to many optimisation problems with other classes of bilinear optimal control problems where the state equation is semilinear and elliptic. We comment on it in a conclusion section. Regarding the geometry of maximisers, we exhibit a blow-up rate for the BV-norm of maximisers as the diffusivity gets smaller: if is an orthotope and if is an optimal control, then The proof of this results relies on a very fine energy argument.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43369074","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: 16

Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms 具有趋化性和一般源项的分层肿瘤生长多相Cahn-Hilliard-Darcy和Cahn-Hilliard-Brinkman模型弱解的存在性

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-05-19 DOI: 10.1080/03605302.2021.1966803

P. Knopf, A. Signori

{"title":"Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms","authors":"P. Knopf, A. Signori","doi":"10.1080/03605302.2021.1966803","DOIUrl":"https://doi.org/10.1080/03605302.2021.1966803","url":null,"abstract":"Abstract We investigate a multiphase Cahn–Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the tumor. Compared to classical two-phase tumor growth models, the multiphase model can be used to describe a stratified tumor exhibiting several layers of tissue (e.g., proliferating, quiescent and necrotic tissue) more precisely. Our model consists of a convective Cahn–Hilliard type equation to describe the tumor evolution, a velocity equation for the associated volume-averaged velocity field, and a convective reaction-diffusion type equation to describe the density of the chemical species. The velocity equation is either represented by Darcy’s law or by the Brinkman equation. We first construct a global weak solution of the multiphase Cahn–Hilliard–Brinkman model. After that, we show that such weak solutions of this system converge to a weak solution of the multiphase Cahn–Hilliard–Darcy system as the viscosities tend to zero in some suitable sense. This means that the existence of a global weak solution to the Cahn–Hilliard–Darcy system is also established.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44614404","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: 12

The Master Equation in a bounded domain with Neumann conditions 具有Neumann条件的有界域上的主方程

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-05-18 DOI: 10.1080/03605302.2021.2008965

M. Ricciardi

引用次数: 6

The mathematical theory of splitting-merging patterns in phase transition dynamics 相变动力学中分裂合并模式的数学理论

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-05-14 DOI: 10.1080/03605302.2022.2053862

Eva Kardhashi, M. Laforest, P. LeFloch

{"title":"The mathematical theory of splitting-merging patterns in phase transition dynamics","authors":"Eva Kardhashi, M. Laforest, P. LeFloch","doi":"10.1080/03605302.2022.2053862","DOIUrl":"https://doi.org/10.1080/03605302.2022.2053862","url":null,"abstract":"Abstract For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is relevant in the theory of phase transition dynamics, and the solutions under consideration enjoy a splitting–merging pattern, consisting of (compressive) classical and (undercompressive) nonclassical waves, interacting together as well as with classical waves of weaker strength. Our analysis is based on three novel ideas. First, a generalization of Hayes–LeFloch’s nonclassical Riemann solver is introduced for systems and is based on prescribing, on one hand, a kinetic relation for the propagation of nonclassical undercompressive shocks and, on the other hand, a nucleation criterion that selects between classical and nonclassical behavior. Second, we extend LeFloch-Shearer’s theorem to systems and we prove that the presence of a nucleation condition implies that only a finite number of splitting and merging cycles can occur. Third, our arguments of nonlinear stability build upon recent work by the last two authors who identified a natural total variation functional for scalar conservation laws and, specifically, for systems of conservation laws we introduce here novel functionals which measure the total variation and wave interaction of nonclassical and classical waves.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46478261","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

Dimension reduction techniques in deterministic mean field games 确定性平均场博弈中的降维技术

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-05-06 DOI: 10.1080/03605302.2021.1998911

J. Lasry, P. Lions, B. Seeger

引用次数: 6

Optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation 一维Cahn-Hilliard方程类碰撞解的最优松弛

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-04-28 DOI: 10.1080/03605302.2021.1987458

S. Biesenbach, R. Schubert, Maria G. Westdickenberg

引用次数: 2