M. Marras, F. Ragnedda, S. Vernier-Piro, V. Vespri
In this note we consider degenerate chemotaxis systems with porous media type diffusion and a source term satisfying the Hadamard growth condition. We prove the Hölder regularity for bounded solutions to parabolic-parabolic as well as for elliptic-parabolic chemotaxis systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper we shall prove the existence, uniqueness and global H$\ddot{o}$lder continuity for the Dirichlet problem of a class of Monge-Ampère type equations which may be degenerate and singular on the boundary of convex domains. We will establish a relation of the H$\ddot{o}$lder exponent for the solutions with the convexity for the domains.
This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling waves, including the sharp type and $C^1$ type semi-finite waves. Our results indicate that chemotaxis slows down the wave speed of semi-finite traveling wave, that is, the traveling wave speed for chemotaxis with porous medium (degenerate) diffusion is smaller than that for the porous medium equation without chemotaxis. As we know, this is a new result not shown in the existing literature. The result appears to be a l…
In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We show the existence of an exponential attractor and, hence, of a finite-dimensional global attractor under certain 'balance conditions' on the order of the degeneracy and the growth of the chemotactic function.
Global entropy solutions to a degenerate parabolic-parabolic chemotaxis system for flux-limited dispersal
本文在有界区域无通量边界条件下，针对通量饱和的退化抛物-抛物趋化系统，利用Schauder不动点定理和有界变差函数方法证明了全局有限时间有界熵解的存在性。
We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect of the initial attractant distribution on bacterial clustering. We prove that the compact support of solutions may shrink if the signal concentration satisfies a special structure, and show the finite speed propagating property without assuming the special structure on attractant concentration, and obtain an explicit formula of the population spreading speed in terms of model parameters. The presented results sugges…
Large time convergence for a chemotaxis model with degenerate local sensing and consumption
本文证明了具有退化局部感知和消耗的趋化模型全局弱解在长期极限下向稳态的收敛性，给出了排除大时间极限为空间齐次的条件，并采用全新方法扩展了先前针对趋化能力函数在零点代数消失情形的结论。
Global boundedness induced by asymptotically non-degenerate motility in a fully parabolic chemotaxis model with local sensing
本文研究了具有局部感知的Keller-Segel型全抛物线趋化模型，通过引入依赖信号的渐近非退化迁移率函数描述排斥主导的趋化性，证明了任意空间维度下经典解的全局有界性，并在迁移率单调非减时验证了向齐次稳态的稳定化。
This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, there by completing previous results on nite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique.
We study a one-dimensional parabolic PDE with degenerate diffusion and non-Lipschitz nonlinearity involving the derivative. This evolution equation arises when searching radially symmetric solutions of a chemotaxis model of Patlak-Keller-Segel type. We prove its local in time wellposedness in some appropriate space, a blow-up alternative, regularity results and give an idea of the shape of solutions. A transformed and an approximate problem naturally appear in the way of the proof and are also crucial in [22] in order to study the global behaviour of solutions of the equation for a critical pa…
This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term $n_t + u\cdot\nabla n =Δn^m - χ\nabla\cdot(n\nabla c) + κn -μn^2$, $x \in Ω,\ t>0$, $c_t + u\cdot\nabla c = Δc - nc$, $x \in Ω,\ t>0$, $u_t + (u\cdot\nabla)u = Δu + \nabla P + n\nablaΦ, \quad \nabla\cdot u = 0$, $x \in Ω,\ t>0$, where $Ω\subset \mathbb{R}^3$ is a bounded domain and $χ,κ\ge 0$ and $m, μ>0$. In the above system without fluid environment Jin (J. Differential Equations, 2017) showed existence and boundedness of global weak solutions. On the other hand, in the above system with $m=1…
Formulation of Chimera Gradient Flows for Chemotaxis Systems with Indirect Signal Production and Degenerate Diffusion
针对无法表示为梯度流的三未知函数抛物趋化系统，将其拆分为三个耦合梯度流，用最小化运动方案构造时间离散近似解，借助Lyapunov泛函保证相对紧性，证明了时间全局解的存在性。
Global existence and boundedness for a degenerate chemotaxis system with indirect signal production via minimizing movement schemes
研究具有间接信号产生的退化趋化系统，通过建立时间离散格式构造弱解，该格式中第一个方程有特定梯度流结构，另两个有\(L^2\)变分结构，利用流交换方法和离散极大正则性证明了弱解的全局存在性和有界性。
We consider non degenerate Brownian SDEs with H{ö}lder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial H{ö}lder continuity assumptions on the drift. Importantly, the estimates reflect the transport of the initial condition by the unbounded drift through an auxiliary, possibly regularized, flow.
This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \begin{align*} \begin{cases} u_t = \nabla\cdot\left(\dfrac{u^p \nabla u}{\sqrt{u^2 + |\nabla u|^2}} \right) -χ\nabla\cdot\left( \dfrac{u^q\nabla v}{\sqrt{1 + |\nabla v|^2}}\right), &x\in Ω,\ t>0, \\[1mm] 0 = Δv - μ+ u, &x\in Ω,\ t>0, \end{cases} \end{align*} where $Ω:= B_R(0) \subset \mathbb{R}^n$ ($n \in \mathbb{N}$) is a ball with some $R>0$, and $χ>0$, $p,q\geq1$, $μ:= \frac 1{|Ω|} \int_Ωu_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--Winkler (Trans.\ Amer.\ Math.\ Soc.\ Ser.\ B;20…
This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \begin{equation*} \begin{cases} u_t = \nabla\cdot\left(\dfrac{u^p \nabla u}{\sqrt{u^2 + |\nabla u|^2}} \right) -χ\nabla\cdot\left(\dfrac{u^q\nabla v}{\sqrt{1 + |\nabla v|^2}}\right), \\[1mm] 0 = Δv - μ+ u \end{cases}\end{equation*} under no-flux boundary conditions in balls $Ω\subset\mathbb{R}^n$, and the initial condition $u|_{t=0}=u_0$ for a radially symmetric and positive initial data $u_0\in C^3(\overlineΩ)$, where $χ>0$ and $μ:=\frac{1}{|Ω|}\int_Ωu_0$. Bellomo--Winkler (Comm.\ Partial Differential Equa…
A class of chemotaxis-Stokes systems generalizing the prototype \[\left\{ \begin{array}{rcl} n_t + u\cdot\nabla n &=& \nabla \cdot \big(n^{m-1}\nabla n\big) - \nabla \cdot \big(n\nabla c\big), c_t + u\cdot\nabla c &=& Δc-nc, u_t +\nabla P &=& Δu + n \nabla ϕ, \qquad \nabla\cdot u =0, \end{array} \right. \] is considered in bounded convex three-dimensional domains, where $ϕ\in W^{2,\infty}(Ω)$ is given. The paper develops an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded…
Application of Orlicz regularity theory in two dimensional chemotaxis systems with logistic sources
本文通过Orlicz空间正则性与变分方法，证明了带logistic源的二维退化趋化系统存在全局解，且logistic源可抑制超线性交叉扩散导致的爆破解。
This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $u_{t}=Δu^{m}$. Our main objective is to improve the H$\ddot{o}$lder estimate obtained by pioneers and then, to show the geometric characteristic of free boundary of degenerate parabolic equation. To be exact, the present work will show that: (1) the weak solution $u(x,t)\in{}C^{α,\fracα{2}}(\mathbb{R}^{n}\times\mathbb{R}^{+})$, where $α\in(0,1)$ when $m\geq2$ and $α=1$ when $m\in(1,2)$; (2) the surface $ϕ=(u(x,t))^β$ is a complete Riemannian manifold, which is …
The asymptotic behavior of solutions to a doubly degenerate chemotaxis-consumption system in the two-dimensional setting
本文针对二维双重退化趋化-消耗系统，通过Moser迭代建立新的Harnack型不等式，补充了系统解的大时间收敛性结果。
Early and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms
本文推导了含退化扩散与密度依赖趋化敏感性的新型趋化模型，克服退化扩散带来的分析困难，分别给出肿瘤细胞迁移早期区域扩张速度估计与晚期稳态指数收敛的结论。
Global well-posedness and flat-hump-shaped stationary solutions for degenerate chemotaxis systems with threshold density
本文研究了退化趋化系统在阈值密度下的全局well-posed性及一维情况下平坦山峰状 stationary 解的构造。
Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms
本文研究退化体积填充趋化系统带源项的初边值问题，在适当假设下证明全局弱解的存在性与唯一性。
$L^\infty$ bounds and asymptotic behavior in a doubly degenerate chemotaxis system below six dimensions
针对三维至五维的双重退化营养趋化系统，该研究证明了特定参数范围内全局一致有界弱解的存在性及长时间行为，所用方法含新型函数不等式、bootstrap论证与Moser迭代法。
This paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates in a two-sided fashion, including an extra nonlinearity represented by a $p$-Laplacian diffusion term. To prove the existence of weak solutions, a Schauder fixed-point argument is applied to a regularized problem and the compactness method is used to pass to the limit. The local Hölder regularity of weak solutions is established using the method of intrinsic scaling. The results are a contribution to showing, qualitatively, to what ext…
We establish strong uniqueness for a class of degenerate SDEs of weak H{ö}rmander type under suitable H{ö}lder regularity conditions for the associated drift term. Our approach relies on the Zvonkin transform which requires to exhibit good smoothing properties of the underlying parabolic PDE with rough, here H{ö}lder, drift coefficients and source term. Such regularizing effects are established through a perturbation technique (forward parametrix approach) which also heavily relies on appropriate duality properties on Besov spaces. For the method employed, we exhibit some sharp thresholds on t…
Global classical solutions to a two-dimensional chemotaxis-fluid system involving signal-dependent degenerate diffusion
本文研究二维信号依赖退化扩散趋化-流体模型，在μ=0时于初始质量小性条件下获得全局经典解，在μ>0时获得全局有界经典解并证明其可收敛到(1,0,0)，从而将无流体系统结果推广到Navier-Stokes流体环境。
Convergence of boundary layers of chemotaxis models with physical boundary conditions~II: Non-degenerate
针对非退化初始数据的消耗型 Keller-Segel 模型，本文通过角部校正、正则化剖面和加权消去技术，证明正扩散解在任意 t>0 收敛至零扩散外层解加边界层解。
On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis
针对模拟多发性硬化症、含非线性扩散率$D(m)$的三方程趋化系统，本文借鉴已有策略证明了在适当假设和正则初值下全局有界解的存在性。
Convergence of boundary layers of chemotaxis models with physical boundary conditions I: degenerate initial data
本文研究一维物理边界条件趋化-流体模型，通过取原函数、Hardy 不等式与加权能量估计，证明小氧气扩散率下边界层解收敛为外层解加内层解。
This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by \begin{equation} \left\{ \begin{array}{l} \displaystyle u_t=\nabla \cdot \Big(\frac{u\nabla u}{\sqrt{u^2+|\nabla u|^2}}\Big) - χ\, \nabla \cdot \Big(\frac{u\nabla v}{\sqrt{1+|\nabla v|^2}}\Big), \\[1mm] 0=Δv - μ+ u, \end{array} \right. \qquad \qquad (\star) \end{equation} under the initial condition $u|_{t=0}=u_0>0$ and no-flux boundary conditions in a ball $Ω\subset R^n$, where $χ>0$ and $μ:=\frac{1}{|Ω|} \int_Ωu_0$. A previous result [3] has…
This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller-Segel system, with the main novelty being that diffusion is nonlinear with flux delimiter features. More precisely, as a prototypical representative of this class we study radially symmetric solutions of the parabolic-elliptic system (see the text). Under the initial condition $u|_{t=0}=u_0>0$ and no-flux boundary conditions in balls $Ω\subset\mathbb{R}^n$, where $χ>0$ and $μ:=\frac{1}{|Ω|} \int_Ωu_0$.\abs The main results assert the existence of a uniqu…
Global solutions to a chemotaxis consumption model involving signal-dependent degenerate diffusion and logistic-type dampening
研究带退化扩散和逻辑阻尼的Keller-Segel消耗系统，在特定参数条件下构造了全局经典解与弱解，并证明弱解的最终光滑性。
This paper is devoted to global existence of weak solutions to the following degenerate kinetic model of chemotaxis \begin{equation} \begin{cases}\label{chemo0} u_t=Δ(γ(v)u) τv_{t}=Δv-v+u \end{cases} \end{equation}in a smooth bounded domain with no-flux boundary conditions. The problem features a positive signal-dependent motility function $γ(\cdot)$ which may vanish as $v$ becomes unbounded. In this paper, we first modify the comparison approach developed recently in \cite{GM,GM2} to derive the upper bounds of $v$ under weakened assumptions on $γ(\cdot)$. Then by introducing a suitable approx…
Chemotaxis compressible Navier-Stokes equations with density-dependent viscosity modeling vascular network formation
本文研究了可压缩纳维-斯托克斯方程与趋化因子反应-扩散方程的耦合，证明了在三维托氏空间中能量有限初始数据下的全局弱解存在性，探讨了趋化力在动量平衡方程中的作用及细胞信号产生机制。
$C^{1,α}$ regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on $C^1$ domains
本文在C^1域上研究带斜边界条件的退化完全非线性椭圆方程，通过先建立几乎C^1平坦域中的一致边界Hölder估计，再利用扰动与紧性方法证明了粘性解直到边界的尖锐C^{1,α}正则性。
Finite-time blow-up in a two species chemotaxis-competition model with degenerate diffusion
本文研究高维球域上带退化扩散的两物种趋化-竞争系统，通过满足矩不等式的弱解框架证明解在有限时间内 L^∞ 范数爆破，并将结果推广到 δ∈(0,1] 的非退化扩散情形。
Hele-Shaw limit of chemotaxis-Navier-Stokes flows
研究趋化-纳维-斯托克斯系统在孔隙介质非线性扩散下的Hele-Shaw极限，证明弱解整体存在性并严格验证极限收敛到自由边界问题。
Bilinear optimal control for chemotaxis model: The case of two-sidedly degenerate diffusion with Volume-Filling Effect
本文针对带体积填充效应的双侧退化扩散趋化反应-扩散耦合系统，在弱框架下研究双线性最优控制问题，证明了直接问题适定性、最优控制存在性与一阶最优性条件，并建立了伴随系统的弱解理论。
We provide here some sharp Schauder estimates for degenerate PDEs of Kolmogorov type when the coefficients lie in some suitable anisotropic H{ö}lder spaces and the first order term is non-linear and unbounded. We proceed through a perturbative approach based on forward parametrix expansions. Due to the low regularizing properties of the degenerate variables, for the procedure to work, we heavily exploit duality results between appropriate Besov spaces. Our method can be seen as constructive and provides, even in the non-degenerate case, an alternative approach to Schauder estimates.
Relationship between haptotaxis and chemotaxis in cell dynamics
本研究探讨了细胞分选中趋触性和趋化性之间的关系，通过分析非局部聚集模型与Keller-Segel型趋化系统之间的联系，揭示了两种机制如何产生相似动态行为。
We consider a Fisher-KPP equation with density-dependent diffusion and advection, arising from a chemotaxis-growth model. We study its behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We analyze, for small times, the emergence of transition layers induced by a balance between reaction and drift effects. Then we investigate the propagation of the layers. Convergence to a free-boundary limit problem is proved and a sharp estimate of the thickness of the layers is provided.
In this paper we consider the initial Neumann boundary value problem for a degenerate Keller--Segel model which features a signal-dependent non-increasing motility function. The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded. In the current work, we are interested in boundedness and exponential stability of the classical solution in higher dimensions. With the aid of a Lyapunov functional and a delicate Alikakos--Moser type iteration, we are able to establish a time-independent upper bound of the concentration provided that the moti…
Absence of dead-core formations in chemotaxis systems with degenerate diffusion
本文证明具有退化扩散和信号消耗的趋化系统在爆破前不会形成死核，并给出经典解的正性保持条件。
We provide here global Schauder-type estimates for a chain of integro-partial differential equations (IPDE) driven by a degenerate stable Ornstein-Uhlenbeck operator possibly perturbed by a deterministic drift, when the coefficients lie in some suitable anisotropic H{ö}lder spaces. Our approach mainly relies on a perturbative method based on forward parametrix expansions and, due to the low regularizing properties on the degenerate variables and to some integrability constraints linked to the stability index, it also exploits duality results between appropriate Besov Spaces. In particular, our…
Avoidance of caldera-type dead cores in a chemotaxis system with degenerate diffusion and compactly supported initial population density
该研究针对具有退化扩散和紧支撑初始种群密度的趋化系统，证明了演化中出现的死核必源自初始零集，给出了死核形成的关键条件。
Refined existence theorems for doubly degenerate chemotaxis-consumption systems with large initial data
本文研究双重退化趋化-消耗系统，通过新的耦合能量型泛函观察和一般不等式，将二维情形下m=2时α的存在性范围从(1,3/2)扩展到(1,2)，并建立了弱解与经典解的全局存在性定理。
Global weak solvability for doubly degenerate nutrient taxis system in physical dimension
研究双退化营养趋化系统在物理维度下的全局弱可解性，针对不同α值划分三种情况，探讨趋化效应强度对解存在性的影响。
Sharp critical mass criteria for weak solutions to a degenerate cross-attraction system
本文研究了全空间中具非线性扩散的两物种耦合抛物-椭圆趋化系统，通过提供精确的二分法准则改进了全局存在与爆破的临界曲线结果，并将单物种Keller-Segel系统的临界质量现象扩展至两物种情形。
Refining Hölder regularity theory in degenerate drift-diffusion equations
本文研究了退化漂diffusion方程中弱解的Hölder正则性，通过引入特定的函数条件和积分约束，证明了有界解的Hölder连续性，并扩展至初边界值问题。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。