Nodea-Nonlinear Differential Equations and Applications最新文献

英文中文

On quasi-linear reaction diffusion systems arising from compartmental SEIR models. 关于分区 SEIR 模型产生的准线性反应扩散系统。

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2024-01-01 Epub Date: 2024-08-06 DOI: 10.1007/s00030-024-00985-w

Juan Yang, Jeff Morgan, Bao Quoc Tang

The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in Viguerie et al. (Appl Math Lett 111:106617, 2021); Viguerie et al. (Comput Mech 66(5):1131-1152, 2020), where the diffusion rate is assumed to depend on the total population, leading to quasilinear diffusion with possible degeneracy. The mathematical analysis of this model has been addressed recently in Auricchio et al. (Math Methods Appl Sci 46:12529-12548, 2023) where it was essentially assumed that all sub-populations diffuse at the same rate, which yields a positive lower bound of the total population, thus removing the degeneracy. In this work, we remove this assumption completely and show the global existence and boundedness of solutions by exploiting a recently developed $L^{p}$ -energy method. Our approach is applicable to a larger class of systems and is sufficiently robust to allow model variants and different boundary conditions.

研究了准线性反应扩散系统解的全局存在性和有界性。该系统源于 Viguerie 等人（Appl Math Lett 111:106617, 2021）和 Viguerie 等人（Comput Mech 66(5):1131-1152, 2020）提出的描述传染病传播的分区模型，其中假定扩散率取决于总人口，从而导致可能存在退化的准线性扩散。最近，Auricchio 等人（Math Methods Appl Sci 46:12529-12548, 2023）对这一模型进行了数学分析，主要假设所有子种群的扩散速率相同，从而得到总种群的正下限，从而消除了退化现象。在这项工作中，我们完全取消了这一假设，并利用最近开发的 L p 能量方法证明了解的全局存在性和有界性。我们的方法适用于更大类别的系统，并具有足够的鲁棒性，允许模型变体和不同的边界条件。

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引用次数: 0

A damped elastodynamics system under the global injectivity condition: local wellposedness in $$L^p$$-spaces 全局注入条件下的阻尼弹性动力学系统:$$L^p$$ -空间中的局部适定性

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-11-04 DOI: 10.1007/s00030-023-00889-1

Sébastien Court

Abstract The purpose of this paper is to model mathematically mechanical aspects of cardiac tissues. The latter constitute an elastic domain whose total volume remains constant. The time deformation of the heart tissue is modeled with the elastodynamics equations dealing with the displacement field as main unknown. These equations are coupled with a pressure whose variations characterize the heart beat. This pressure variable corresponds to a Lagrange multiplier associated with the so-called global injectivity condition. We derive the corresponding coupled system with nonhomogeneous boundary conditions where the pressure variable appears. For mathematical convenience a damping term is added, and for a given class of strain energies we prove the existence of local-in-time solutions in the context of the $$L^p$$ L p -parabolic maximal regularity.

摘要本文的目的是对心脏组织的力学方面进行数学建模。后者构成了一个总积保持恒定的弹性域。采用以位移场为主要未知量的弹性动力学方程来模拟心脏组织的时间变形。这些方程式与压力相结合，压力的变化是心跳的特征。这个压力变量对应于与所谓的全局注入条件相关的拉格朗日乘数。导出了具有压力变量的非齐次边界条件下的耦合系统。为了数学上的方便，我们增加了一个阻尼项，并且对于给定的应变能，我们证明了在$$L^p$$ L p -抛物极大正则性条件下局部解的存在性。

引用次数: 0

Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold 接触子黎曼流形中超曲面的内禀子拉普拉斯

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-26 DOI: 10.1007/s00030-023-00891-7

Davide Barilari, Karen Habermann

Abstract We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact sub-Riemannian manifold. We prove that, away from characteristic points, the intrinsic sub-Laplacian arises as the limit of Laplace–Beltrami operators built by means of Riemannian approximations to the sub-Riemannian structure using the Reeb vector field. We carefully analyse three families of model cases for this setting obtained by considering canonical hypersurfaces embedded in model spaces for contact sub-Riemannian manifolds. In these model cases, we show that the intrinsic sub-Laplacian is stochastically complete and in particular, that the stochastic process induced by the intrinsic sub-Laplacian almost surely does not hit characteristic points.

构造并研究了嵌入在接触子黎曼流形中的光滑超曲面的特征点集外的内禀子拉普拉斯算子。我们证明了在远离特征点的地方，内禀子拉普拉斯算子是利用Reeb向量场对子黎曼结构进行黎曼逼近所建立的拉普拉斯-贝尔特拉米算子的极限。我们仔细分析了通过考虑嵌入在接触亚黎曼流形模型空间中的正则超曲面而得到的这种设置的三种模型情况。在这些模型情况下，我们证明了内禀子拉普拉斯算子是随机完备的，特别是，由内禀子拉普拉斯算子引起的随机过程几乎肯定不会击中特征点。

引用次数: 1

Pushed fronts in a Fisher–KPP–Burgers system using geometric desingularization 使用几何去具体化的Fisher-KPP-Burgers系统中的推锋

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-20 DOI: 10.1007/s00030-023-00890-8

Matt Holzer, Matthew Kearney, Samuel Molseed, Katie Tuttle, David Wigginton

引用次数: 0

A family of nonlocal degenerate operators: maximum principles and related properties 一类非局部退化算子:极大原理及相关性质

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-19 DOI: 10.1007/s00030-023-00892-6

Delia Schiera

引用次数: 0

A Relation of the Allen–Cahn equations and the Euler equations and applications of the equipartition Allen-Cahn方程与Euler方程的关系及均分的应用

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-06 DOI: 10.1007/s00030-023-00888-2

Dimitrios Gazoulis

Abstract We will prove that solutions of the Allen–Cahn equations that satisfy the equipartition of the energy can be transformed into solutions of the Euler equations with constant pressure. As a consequence, we obtain De Giorgi type results, that is, the level sets of entire solutions are hyperplanes. Also, we will determine the structure of solutions of the Allen–Cahn system in two dimensions that satisfy the equipartition. In addition, we apply the Leray projection on the Allen–Cahn system and provide some explicit entire solutions. Finally, we obtain some examples of smooth entire solutions of the Euler equations. For specific type of initial conditions, some of these solutions can be extended to the Navier–Stokes equations. The motivation of this paper is to find a transformation that relates the solutions of the Allen–Cahn equations to solutions of the minimal surface equation of one dimension less. We prove this result for equipartitioned solutions in dimension three.

摘要证明了满足能量均分的Allen-Cahn方程的解可以转化为恒压条件下的Euler方程的解。因此，我们得到了De Giorgi型结果，即整个解的水平集是超平面。同时，我们将确定满足均分的二维Allen-Cahn系统的解的结构。此外，我们将Leray投影应用于Allen-Cahn系统，并给出了一些显式全解。最后，给出了欧拉方程光滑全解的一些例子。对于特定类型的初始条件，其中一些解可以推广到Navier-Stokes方程。本文的动机是寻找一种将Allen-Cahn方程的解与一维最小曲面方程的解联系起来的变换。我们在三维的等分解中证明了这个结果。

引用次数: 1

Harmonic embeddings of the Stretched Sierpinski Gasket 拉伸席尔平斯基垫片的谐波嵌入

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-04 DOI: 10.1007/s00030-023-00877-5

Ugo Bessi

引用次数: 0

Existence and non-existence results for a semilinear fractional Neumann problem 一类半线性分数阶Neumann问题的存在性与不存在性结果

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-03 DOI: 10.1007/s00030-023-00886-4

Eleonora Cinti, Francesca Colasuonno

Abstract We establish a priori $$L^infty $$ L ∞ -estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficient and on the nonlinearity. Moreover, we prove an existence result for radial, radially non-decreasing solutions in the case of a possible supercritical nonlinearity, extending to the case $$0 0 < s ≤ 1 / 2 the analysis started in [7].

摘要建立了一类半线性非局部Neumann问题非负解的先验$$L^infty $$ L∞估计。根据这些估计，在适当的扩散系数和非线性假设下，我们得到了非常解的不存在性。此外，我们证明了在可能的超临界非线性情况下径向非递减解的存在性结果，并推广到$$0<sle 1/2$$ 0 ＆lt;S≤1 / 2，从[7]开始分析。

引用次数: 1

Nonlinear dynamic problems for 2D magnetoelastic waves 二维磁弹性波的非线性动力学问题

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-09-25 DOI: 10.1007/s00030-023-00887-3

Viatcheslav Priimenko, Mikhail Vishnevskii

引用次数: 0

Asymptotic mean value properties for the elliptic and parabolic double phase equations 椭圆型和抛物型双相方程的渐近均值性质

4区数学 Q2 Mathematics

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-09-20 DOI: 10.1007/s00030-023-00884-6

Weili Meng, Chao Zhang

引用次数: 0

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