Evangelos Latos, Takashi Suzuki
We study quasilinear reaction diffusion systems relative to the Shigesada-Kawasaki-Teramoto model. Nonlinearity standing for the external force is provided with mass dissipation. Estimate in several norms of the solution is provided under the restriction of diffusion coefficients, growth rate of reaction, and space dimension.
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 work we analyze the solutions of a $p$-Laplacian equation with homogeneous Neumann boundary conditions set in a family of rough domains with a nonlinear term concentrated on the boundary. At the limit, we get a nonlinear boundary condition capturing the oscillatory geometry of the strip where the reactions take place.
We study the behaviour of nonnegative solutions to the quasilinear heat equation with a reaction localized in a ball $$ u_t=Δu^m+a(x)u^p, $$ for $m>0$, $0<p\le\max\{1,m\}$, $a(x)=\mathds{1}_{B_L}(x)$, $0<L<\infty$ and $N\ge2$. We study when solutions, which are global in time, are bounded or unbounded. In particular we show that the precise value of the length $L$ plays a crucial role in the critical case $p=m$ for $N\ge3$. We also obtain the asymptotic behaviour of unbounded solutions and prove that the grow-up rate is different in most of the cases to the one obtained when $L=\infty$.
We study the behaviour of global solutions to the quasilinear heat equation with a reaction localized $$ u_t=(u^m)_{xx}+a(x) u^p, $$ $m, p>0$ and $a(x)$ being the characteristic function of an interval. we prove that there exists $p_0=\max\{1,\frac{m+1}2\}$ such that all global solution are bounded if $p>p_0$, while for $p\le p_0$ all the solution are global and unbounded. In the last case, we prove that if $p<m$ the grow-up rate is different to the one obtained when $a(x)\equiv1$, while if $p>m$ the grow-up rate coincides with that rate, but only inside the support of $a$; outside the interva…
Separable solutions of some quasilinear equations with source reaction
研究了一类带反应项的拟线性方程奇异可分解的存在性。在二维情形下，我们使用动力系统方法来构造解。
We study the equation --div(A(x, u)) = g(x, u, u) + $μ$ where $μ$ is a measure and either g(x, u, u) $\sim$ |u| q 1 u||u| q 2 or g(x, u, u) $\sim$ |u| s 1 u + ||u| s 2. We give sufficient conditions for existence of solutions expressed in terms of the Wolff potential or the Riesz potentials of the measure. Finally we connect the potential estimates on the measure with Lipchitz estimates with respect to some Bessel or Riesz capacity.
Limiting behavior of quasilinear wave equations with fractional-type dissipation
本文研究具有时间非局部耗散的Westervelt型拟线性波方程，在记忆核弱奇异的最小假设下证明其适定性，并分析小参数趋于零时解的极限行为。
We prove existence and uniqueness of self-similar solutions with exponential form $$ u(x,t)=e^{αt}f(|x|e^{-βt}), \qquad α, \ β>0 $$ to the following quasilinear reaction-diffusion equation $$ \partial_tu=Δu^m+|x|^σu^p, $$ posed for $(x,t)\in\real^N\times(0,T)$, with $m>1$, $1<p<m$ and $σ=-2(p-1)/(m-1)$ and in dimension $N\geq2$, the same results holding true in dimension $N=1$ under the extra assumption $1<p<(m+1)/2$. Such self-similar solutions are usually known in literature as \emph{eternal solutions} since they exist for any $t\in(-\infty,\infty)$. As an application of the existence of the…
We study the blow up profiles associated to the following second order reaction-diffusion equation with non-homogeneous reaction: $$ \partial_tu=\partial_{xx}(u^m) + |x|^σu, $$ with $σ>0$. Through this study, we show that the non-homogeneous coefficient $|x|^σ$ has a strong influence on the blow up behavior of the solutions. First of all, it follows that finite time blow up occurs for self-similar solutions $u$, a feature that does not appear in the well known autonomous case $σ=0$. Moreover, we show that there are three different types of blow up self-similar profiles, depending on whether th…
Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction
该研究针对带加权反应的拟线性反应扩散方程，分类了自相似形式的爆破解，揭示了非齐次权重对爆破模式的影响，丰富了反应扩散方程爆破行为的研究。
Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups
本文研究Carnot群上带指数反应和测度数据的拟线性方程，建立了非负解的存在性和逐点Wolff势界，覆盖次临界与临界情形。
On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems
本文证明吉因斯-兰道方程能准确预测准线性模式形成反应-扩散-对流系统的动力学，并应用于格雷-斯科特-克劳斯梅尔模型。
Quasilinear and Hessian type equations with exponential reaction and measure data
本文证明了在有界区域$Ω$或整个$\mathbb{R}^N$中$-Δ_pu=P(u)+μ$型方程对于$p>1$和$F_k[-u]=P(u)+μ$ with $1\leq k<\frac{N}{2}$的存在性结果，其中$μ$是正Radon测度，而$P(u)\sim e^{au^β}$ with $a>0$和$β\geq 1$ .存在的充分条件表示在$μ$的分数极大潜力。利用$μ$的一些精确Wolff势，得到了解的双边估计.根据Orlicz容量得到了必要条件。我们还在$\mathbb{R}^N$中建立了形式为$u={\bf W}_{α,p}^R[P(u)]+f$的一般Wolff势方程的存在性结果，其中0
We discuss a multiscale Galerkin approximation scheme for a system of coupled quasilinear parabolic equations. These equations arise from the upscaling of a pore scale filtration combustion model under the assumptions of large Damkhöler number and small Péclet number. The upscaled model consists of a heat diffusion equation and a mass diffusion equation in the bulk of a macroscopic domain. The associated diffusion tensors are bivariate functions of temperature and concentration and provide the necessary coupling conditions to elliptic-type cell problems. These cell problems are characterized b…
Group classification of variable coefficient quasilinear reaction-diffusion equations
对变系数拟线性反应扩散方程组$u_t=u_{xx}+h(x)B(u)$进行了详尽的群分类。这成为可能，由于使用的条件等价组中发现的过程中的研究容许点变换类内。
Quasilinear parabolic reaction-diffusion systems: user's guide to well-posedness, spectra and stability of travelling waves
本文研究了扩张区域上的拟线性抛物型反应扩散平流方程组。在希尔伯特空间和连续函数空间中的适定性的框架，基于已知的结果使用最大正则性。它示出，谱线上的行波有意义地给出了熟悉的工具，半线性方程，如色散关系，并考虑基本连接的谱的稳定性和不稳定性。特别地，证明了平衡流形的线性化轨道不稳定性原理。我们的目标是为申请人提供轻松访问这些严格的方面。作为一个指导性的例子，格雷斯科特-克劳斯迈尔模型的植被-水的相互作用被认为是详细的。
On quasilinear parabolic evolution equations in weighted Lp-spaces II
本文将文[17]中关于时间加权L_p-空间中抽象拟线性抛物问题的研究推广到包含奇异低阶项，同时保持较低的初始正则性。结果适用于反应扩散问题，包括麦克斯韦-斯特凡扩散，和几何发展方程一样的表面扩散流或Willmore流。本文的方法也适用于其它抛物型方程组，包括自由边界问题。
Existence of blow-up self-similar solutions for the supercritical quasilinear reaction-diffusion equation
本文证明了超临界拟线性反应扩散方程在特定条件下存在有限时间爆破的自相似解，并揭示了Lepin临界指数在自相似爆破解存在性上的非最优性。
No pattern formation in a quasilinear chemotaxis model with local sensing
本文证明了在局部感知趋化模型中，当内在扩散速率与趋化运动函数满足特定条件时，空间齐次稳态的收敛性，从而排除了图案形成，并符合已有研究。
Optimal existence, uniqueness and blow-up for a quasilinear diffusion equation with spatially inhomogeneous reaction
本文研究具有空间非齐次反应项的拟线性扩散方程，确定了初始条件的最优类以保证局部存在性与唯一性，并证明非平凡解有限时间爆破、有限传播速度及爆破时无局部化。
Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth
本文研究了具有质量耗散和二次增长的正性保持反应扩散系统的Neumann和Cauchy问题，证明了在任意空间维度下全局经典解的存在性，推广了先前在n≥3维度下需质量守恒且限于Cauchy问题的结果，且证明更简单。
Boundedness and evolution rates for a quasilinear reaction-diffusion equation
研究N≥3维空间中指数1<p<m且σ<-2的拟线性反应扩散方程，证明初始条件满足一定衰减时解一致有界，并建立了紧支集数据正性集上界R(t)的扩张速率及外部区域的不同时间尺度。
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if the diffusion coefficients are close to each other, or if the diffusion coefficients are large enough compared to initial data, then the local classical solution exists globally and is bounded uniformly in time. Applications of the results include the validity of the Global Attractor Conjecture for complex balanced reaction systems with large diffusion.
A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario
本文研究多孔介质中描述胶体粒子扩散、聚集和沉积的多尺度拟线性反应扩散系统的弱可解性，利用 Schauder 不动点定理证明解的存在性并提供收敛算法，数值模拟展示了近堵塞场景下的浓度行为。
We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, the interplay between chemical diffusion and fluid transportation causes the enhanced dissipation phenomenon. We show that the enhanced dissipation time scale, together with the reaction coupling strength, determines the characteristic time scale of the reaction.
Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly super-) quadratic growth. This pushes forward the recent advances concerning global existence of reaction-diffusion systems dissipating mass in which a uniform-in-time bound has been known only in space dimension one or two. As an application, skew-symmetric Lotka-Volterra systems are shown to have unique classical solutions which are uniformly bounded in t…
The Kuznetsov and Blackstock equations of nonlinear acoustics with nonlocal-in-time dissipation
本文研究含分数阶时间非局部耗散的 Kuznetsov 与 Blackstock 方程，给出记忆核最小假设，并证明关于小参数一致的适定性及能量范数收敛速率。
We study the behaviour of the solutions to the quasilinear heat equation with a reaction restricted to a half-line $$ u_t=(u^m)_{xx}+a(x) u^p, $$ $m, p>0$ and $a(x)=1$ for $x>0$, $a(x)=0$ for $x<0$. We first characterize the global existence exponent $p_0=1$ and the Fujita exponent $p_c=m+2$. Then we pass to study the grow-up rate in the case $p\le1$ and the blow-up rate for $p>1$. In particular we show that the grow-up rate is different as for global reaction if $p>m$ or $p=1\neq m$.
Stabilization of Quasilinear Parabolic Equations by Cubic Feedback at Boundary with Estimated Region of Attraction
本文针对开环有限时间爆破解的拟线性抛物方程，提出边界三次反馈镇定方法，保证指数稳定性、解收敛及正性，并估计吸引域，其大小随扩散增强而增大。
Non-concentration phenomenon for one dimensional reaction-diffusion systems with mass dissipation
本文针对一维质量耗散反应扩散系统，移除额外熵假设，通过证明 Morrey 空间中的非集中现象，建立三次乃至略微超三次中间和条件下解的全局有界性。
Diffusive stability of oscillations in reaction-diffusion systems
研究了反应扩散系统空间齐次振动的非线性稳定性。假设中性相不存在不稳定的线性模和线性扩散行为，我们证明了空间局域扰动在空间维n上以代数方式衰减，扩散速率为t^{-n/2}。我们还计算了解决方案的渐近展开中的领先阶项，并表明它对应于相位的空间局部调制。我们的方法是基于动力学常微分方程的正常形式的转换，其中部分的相方程，在整个系统的准线性的代价。稳定性，然后获得了一个整体的不动点参数在时间加权索伯列夫空间。
A new class of quasilinear reaction-diffusion equations is introduced for which the mass flow never reaches the boundary. It is proved that the initial value problem is well-posed in an appropriate weighted Sobolev space setting.
We investigate quasilinear discrete PDEs $\partial_t u = Δ^N φ(u)+ Kf(u)$ of reaction-diffusion type with nonlinear diffusion term defined on an $n$-dimensional unit torus discretized with mesh size $\tfrac1N$ for $N\in {\mathbb N}$, where $Δ^N$ is the discrete Laplacian, $φ$ is a strictly increasing $C^5$ function and $f$ is a $C^1$ function. We establish $L^\infty$ bounds and space-time Hölder estimates, both uniform in $N$, of the first and second spatial discrete derivatives of the solutions. In the equation, $K>0$ is a large constant and we show how these estimates depend on $K$. The moti…
Well-posedness and qualitative properties of quasilinear degenerate evolution systems
本文研究了生物膜生长等背景下的非线性退化耦合 PDE-PDE 和 PDE-ODE 系统，通过正则化与不动点论证证明了弱解存在性与唯一性，确立了不同边界条件下的全局或局部适定性，并给出了解的有限时间爆破或一致有界性条件及全局正则性。
Well-Posedness for Fractional Reaction-Diffusion Systems with Mass Dissipation in $\mathbb R^N$
本文研究全空间中带质量耗散的分数阶反应扩散系统的适定性，证明了二次非线性项下解的全局唯一有界性，以及超二次非线性项满足中间和条件时解的全局存在性，拓展了相关理论到非局部扩散无界域情形。
Two-phase forward solutions for one-dimensional forward-backward parabolic equations with linear convection and reaction
研究了一类带线性对流和反应的一维拟线性向前向后扩散方程Neumann边值问题的Lipschitz连续弱解的存在性和性质.扩散通量函数被假定为包含两个前向扩散阶段的前向-后向类型。证明了对于所有光滑初值，至少存在一个弱解，其空间导数处于两个正向相位。此外，对于所有光滑的初始数据，有一个导数值位于一定的相变范围内，我们表明，存在无限多个这样的解决方案，表现出两个前向相位之间的瞬时相变。此外，我们引入了过渡规范的概念，这样的前向解决方案，并证明了所有构造的两相前向解决方案的规范可以任意接近某一固定常数。
Traveling waves of a reaction-diffusion system with partially coupled diffusion
研究具有部分耦合扩散的反应扩散系统的行波解，在第一个分量不扩散时进行理论分类，两个分量都扩散时进行数值研究，应用于捕食者 - 猎物和流行病学等模型。
Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches
证明了带p-Laplacian算子的四阶拟线性反应扩散方程允许三种类型的爆破.自相似模式首先构造的区域爆破的情况下，重新标度的问题承认一个变分设置。接下来，通过分支方法将这些扩展到非变分问题。
Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems
本文利用 EDP 收敛理论刻画慢-快梯度系统的非平衡稳态为固定慢变量时 Lagrangian 的鞍点，并在反应-扩散与薄膜极限中给出应用。
Global classical solutions by transport noise for reaction-diffusion systems with entropy dissipation
针对确定性框架下反应扩散系统全局经典解存在性的开放问题，该文证明适当输运噪声可使复杂平衡化学反应网络生成时间全局的唯一强解，还能按指定速率增强空间涨落耗散，证明结合了多种分析方法。
Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity
本文研究扩散系数兼具多孔介质型退化与奇异性的拟线性反应扩散方程柯西问题，利用m-增生算子理论、动力学公式和Fourier分析技术证明了其适定性与Sobolev正则性。
We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the literature and thus allows the nonlinearities to have arbitrary polynomial growth. We show that two dimensional reaction-diffusion systems, with quadratic intermediate sum conditions, have global solutions which are bounded uniformly in time. In higher dimension, bounded solutions are obtained under the condition that the diffusion coefficients are {\it quasi-unifo…
Reaction-diffusion systems of Maxwell-Stefan type with reversible mass-action kinetics
对单相多组分反应混合物的基于质量的Maxwell-Stefan方法进行了数学分析。结果表明，所得到的拟线性，强耦合的反应扩散系统是局部适定的$L_p$设置，并产生一个局部半流的自然状态空间。如果解的初始分量都是非负且非平凡的，则解立即正则化并变为严格正的。对于一类可逆的质量作用动力学，确定了正平衡：这些正是系统的恒定化学平衡，可以形成一个流形。这里采用系统的总自由能作为系统的李雅普诺夫函数。利用广义线性稳定性原理，证明了正平衡点通常稳定。
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. The weak-strong uniqueness principle holds for dissipative renormalised solutions, which in addition to the renormalised formulation obey suitable dissipation inequalities consistent with previous existence results. We treat general entropy-dissipating reactions without growt…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be measurable and uniformly bounded. The nonlinearities are quasi-positive and satisfy a commonly called mass control or dissipation of mass property. Moreover, we assume the intermediate sum condition of a certain order. The key feature of this work is the surprising discovery that quasi-positive systems that satisfy an intermediate sum condition automatically g…
Exponential decay towards equilibrium and global classical solutions for nonlinear reaction-diffusion systems
我们考虑一个系统的反应扩散方程描述的可逆反应的两个物种$\mathcal{U}, \mathcal{V}$形成第三物种$\mathcal{W}$，反之亦然，根据质量作用定律动力学与任意的化学计量系数（等于或大于1）。首先，在$\mathcal{U}$或$\mathcal{V}$的扩散系数之一充分接近于$\mathcal{W}$的扩散系数的条件下，利用改进的对偶估计证明了整体经典解的存在性.其次，我们得到了一个熵耗散估计，即一个函数不等式，应用于这些反应扩散系统的整体解，证明了指数收敛到平衡点，具有显式的速率和常数。
On quasi-linear reaction diffusion systems arising from compartmental SEIR models
本文研究了源自分区 SEIR 模型的拟线性反应扩散系统，通过引入 $L^p$-能量方法去除了所有子种群以相同速率扩散的假设，证明了解的全局存在性与有界性，且该方法适用于更广泛的系统类别及不同边界条件。
The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass control, which includes the important cases as mass conservation and mass dissipation. Under these assumptions, the local classical solution is shown to be global and, in case of mass conservation or mass dissipation, to have $L^{\infty}$-norm growing at most polynomially in time. Applications include skew-symmetric Lotka-Volterra systems and quadratic reversible…
Trend to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks
利用熵方法研究了具有质量作用动力学的复杂平衡化学反应网络的反应扩散系统向平衡态的定量收敛性。在本文的第一部分中，通过显式地导出熵耗散，我们证明了对于没有边界平衡点的复杂平衡系统，每个轨迹都指数快速地收敛到唯一的复杂平衡点。此外，一个建设性的证明，提出了明确估计的收敛速率的特殊情况下的循环反应。第二部分研究了具有边界平衡点的复杂平衡系统。我们调查两个具体的情况下，分别具有两个和三个化学物质。在这些情况下，边界平衡点在某种意义上是不稳定的，因此也可以证明指数收敛到唯一的严格正平衡点。
Explicit exponential convergence to equilibrium for nonlinear reaction-diffusion systems with detailed balance condition
研究了由化学反应网络产生的质量作用反应扩散系统的平衡收敛性。所考虑的反应网络被假定为满足详细的平衡条件，没有边界平衡。我们提出了一种通用的方法，基于所谓的熵的方法，这是能够量化与明确计算率的熵泛函的衰减的熵熵耗散不等式的基础上的整体的守恒律的系统。因此，以下收敛到唯一的详细平衡平衡明确可计算的收敛速度。一般的方法是进一步详细的两个重要的示例系统：一个单一的可逆反应，涉及任意数量的化学物质和链的两个可逆反应所产生的酶反应。
Solutions of the 4-species quadratic reaction-diffusion system are bounded and $C^\infty$, in any space dimension
我们建立了具有二次（实际上是略超二次）反应项的反应扩散系统的解的有界性，这些反应项满足自然熵耗散性质，在任何空间维度N>2。这个界意味着解的光滑性。这一结果推广了仅限于二维情形的理论。证明大量使用De Giorgi的迭代方案，这使我们能够获得局部估计。参数依赖于对偶推理，以获得新的估计系统的总质量，无论是在$L^{(N+1)/N}$规范和在一个适当的弱规范。后者使用$C^α$正则化性质的抛物型方程。
Another look at quasilinear Schrödinger equations with prescribed mass via dual method
本文通过双重方法研究具有给定质量的准线性Schrödinger方程的基态归一化解的存在性及性质。
Global classical solutions for mass-conserving, (super)-quadratic reaction-diffusion systems in three and higher space dimensions
本文考虑二次和超二次反应扩散系统的可逆化学，其中所有物种满足均匀的时间$L^1$先验估计，例如，作为适当的质量守恒定律的结果。利用Bochner空间中的正则性和插值论证，Bootstrap方法和弱比较论证，在三维及高维空间中证明了经典解的整体存在性.此外，所考虑的系统允许熵熵耗散估计证明指数收敛到平衡，我们也能够证明，解决方案有界均匀的时间。
Some qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction
本研究针对带加权强反应的拟线性反应扩散方程柯西问题，分$m+p\geq2$和$m+p<2$两种参数范围，证明了解的存在性、支集传播速度特性及多解性等定性性质，并建立了新的Aronson-Bénilan先验估计。
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or ef…
Discrete-to-continuum limit for nonlinear reaction-diffusion systems via EDP convergence for gradient systems
本文针对满足细致平衡条件的质量作用定律反应扩散系统，构造空间离散过程，证明解与梯度系统层面的离散到连续收敛，并通过链式法则不等式和变分方法实现。
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。