Journal of Differential Equations最新文献

英文中文

Increasing stability for inverse acoustic source problems in the time domain 提高时域反声源问题的稳定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114114

Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

This paper is concerned with the inverse source problems for the acoustic wave equation in the full space

R^{3}

, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the

L^{2}

-norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.

本文研究了全空间R3中声源项在时间和空间变量上均紧支持的声波方程的逆源问题。主要目标是根据给定参数的间隔长度（例如，源函数的时间分量的频带）来研究波动方程的稳定性。我们只用狄利克雷边界数据建立了源函数l2范数的渐增稳定性估计。我们的方法依赖于惠更斯原理、傅里叶变换和解析函数延拓的显式界。

引用次数: 0

Half-space theorems for translating solitons of the r-mean curvature flow r-平均曲率流的平移孤子的半空间定理

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114115

Hilário Alencar , G. Pacelli Bessa , Gregório Silva Neto

In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the

(r - 1)

-mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the

(r - 1)

-mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the

(r - 1)

-mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.

本文在(r−1)-平均曲率和第二基本形式的范数上，建立了适当生长条件下r-平均曲率流的完全平移孤子的不存在性结果。我们首先证明了这样的孤子不能完全包含在对称轴与平移方向对齐的右旋转锥的补中。然后我们放宽了(r−1)-平均曲率上的生长条件，并证明了适当浸入的平移孤子不能局限于与平移方向相反的某些半空间。我们通过证明在(r−1)-平均曲率上满足适当生长条件的完全的、适当浸入的平移孤子不能完全位于两个横向垂直半空间的交点内来结束本文。

引用次数: 0

Smoothing property assumptions for uniformly differential processes acting on time-dependent normed spaces 作用于时相关赋范空间的一致微分过程的平滑性假设

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114103

Tomás Caraballo , Alexandre N. Carvalho , Arthur C. Cunha , Heraclio López-Lázaro

In this paper, we introduce the concept of uniformly differentiable evolution processes for dynamical systems on families of time-dependent phase spaces. This framework is motivated by two main aspects: it provides an appropriate framework for studying the dynamics of solutions to non-cylindrical PDE problems, and it naturally extends the theory of uniformly differentiable evolution processes on fixed phase spaces. We establish sufficient conditions on the differential of the evolution process, decomposed as the sum of a contraction and an operator with compactness properties, ensuring that the associated pullback attractors have finite fractal dimension. Our approach is inspired by the smoothing property, Mañé's method, and techniques for controlling backward bounded trajectories. As an application, we analyze non-cylindrical problems with different geometries, studying the dynamics of solutions for the one-dimensional semilinear heat equation and for the two-dimensional Navier-Stokes equations.

本文引入了时变相空间族上动力系统一致可微演化过程的概念。该框架的动机主要有两个方面：它为研究非圆柱形PDE问题解的动力学提供了一个合适的框架，并且自然地扩展了固定相空间上一致可微演化过程的理论。我们建立了演化过程的微分的充分条件，将其分解为具有紧性的收缩算子和算子，从而保证了相关的回拉吸引子具有有限的分形维数。我们的方法受到平滑特性、Mañé的方法和控制后向有界轨迹的技术的启发。作为应用，我们分析了不同几何形状的非圆柱形问题，研究了一维半线性热方程和二维Navier-Stokes方程解的动力学。

引用次数: 0

Global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction 具有双曲热传导的可压缩Navier-Stokes方程的全局适定性和大时性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114111

Fucai Li , Houzhi Tang , Shuxing Zhang

The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction named Cattaneo's law was proposed, which leads to the finite speed of heat propagation. A natural question is whether the large-time behavior of the heat flux for compressible flow would be different for these two laws. In this paper, we aim to address this question by studying the global well-posedness and the optimal time-decay rates of classical solutions to the compressible Navier-Stokes system with Cattaneo's law. By designing a new method, we obtain the optimal time-decay rates for the highest order derivatives of the heat flux, which cannot be derived for the system with Fourier's law by Matsumura and Nishida (1979) [25]. In this sense, our results first reveal the essential differences between the two laws.

经典的傅立叶定律指出热流密度与温度梯度成正比，这导致了热传导的无限传播速度悖论。为了准确地模拟真实的物理过程，提出了热传导的双曲模型，即Cattaneo定律，该定律导致热传播速度有限。一个自然的问题是，对于这两个定律，可压缩流的热通量的大时间行为是否会有所不同。本文通过研究具有Cattaneo定律的可压缩Navier-Stokes系统经典解的全局适定性和最优时间衰减率来解决这一问题。通过设计一种新的方法，我们得到了Matsumura和Nishida(1979)[25]用傅立叶定律无法得到的系统最高阶导数的最优时间衰减率。从这个意义上说，我们的结果首先揭示了两个定律之间的本质区别。

引用次数: 0

Complex spatiotemporal dynamics in a diffusive intraguild predation model with digestion delay 具有消化延迟的扩散性捕食模型的复杂时空动力学

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114107

Wanxiao Xu , Hongying Shu , Lin Wang , Xiang-Sheng Wang , Jianshe Yu

Incorporating spatial diffusion and digestion delay into an intraguild predation (IGP) model, this work demonstrates rich spatiotemporal dynamics governing biological invasions. We derive criteria for the successful invasion of the intraguild predator and identify a critical diffusion threshold that eliminates spatially heterogeneous steady states. The digestion delay induces stability switches, resulting in a finite number of stability intervals, and causing abrupt shifts in coexistence patterns as the delay crosses critical thresholds. Through steady state bifurcation analysis, we rigorously establish the emergence of spatially heterogeneous coexistence states. We further derive Turing instability conditions for Hopf-bifurcating periodic solutions in a general three-dimensional delayed diffusive system. Our results reveal multiple coexistence mechanisms, including homogeneous steady states, periodic oscillations, and complex spatiotemporal patterns, highlighting the intricate interplay between time delay and spatial heterogeneity in biological invasions.

将空间扩散和消化延迟纳入到一个种群内捕食（IGP）模型中，这项工作展示了控制生物入侵的丰富时空动态。我们推导了野生捕食者成功入侵的标准，并确定了消除空间异质稳态的关键扩散阈值。消化延迟诱导稳定开关，导致有限数量的稳定间隔，并在延迟超过临界阈值时引起共存模式的突变。通过稳态分岔分析，我们严格地建立了空间异质共存状态的出现。在此基础上，进一步导出了一类广义三维延迟扩散系统hopf分岔周期解的图灵不稳定性条件。我们的研究结果揭示了生物入侵的多重共存机制，包括均匀的稳态、周期振荡和复杂的时空模式，突出了生物入侵的时间延迟和空间异质性之间复杂的相互作用。

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引用次数: 0

Global smooth solutions of compressible Navier–Stokes equations with degenerate viscosity and vacuum 具有退化黏度和真空的可压缩Navier-Stokes方程的全局光滑解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114112

Andrew Yang , Xu Zhao , Wenshu Zhou

We study free boundary problem of the one dimensional compressible isentropic Navier–Stokes equations with density–dependent viscosity when the initial density connects to the vacuum states continuously and is either of compact or infinite support. Precisely, the pressure and the viscosity coefficient are assumed to be proportional to

ρ^{γ}

and

ρ^{θ}

respectively, where ρ is the density, and γ and θ are positive constants. We prove the global existence of smooth solutions with large initial data when

θ > 0

and

γ \geq 1 + θ

. Since the power θ of the previous results on this topic does not exceed 2, the result of this paper fills at least the gap for large θ. The result includes also the case of the infinite support of the initial density, which just corresponds to the one when

0 < θ \leq 1

. Notice that two key estimates of the proof are the uniform lower bound of the density and the uniform

L^{\infty}

bound of the velocity with respect to the construction of the approximate solutions. In contrast to the traditional techniques relying on weighted energy estimates, they are proved independently by the comparison principle and the maximal principle, respectively. Moreover, we obtain some results on regularity up to boundary and uniqueness of solutions. The results of this paper cover some important models, for instance, the viscous Saint–Venant model for the motion of shallow water, i.e.,

θ = 1

and

γ = 2

研究了初始密度与真空状态连续连接且为紧支撑或无限支撑时，具有密度依赖黏度的一维可压缩等熵Navier-Stokes方程的自由边界问题。精确地说，假设压力和粘度系数分别与ργ和ρθ成正比，其中ρ为密度，γ和θ为正常数。证明了当θ>；0和γ≥1+θ时具有大初始数据的光滑解的整体存在性。由于这一主题的先前结果的幂θ不超过2，因此本文的结果至少填补了大θ的空白。结果还包括初始密度的无限支撑情况，它正好对应于0<；θ≤1时的情况。注意，证明的两个关键估计是密度的均匀下界和速度的均匀L∞界，这是关于近似解的构造的。与传统的依赖加权能量估计的方法不同，它们分别通过比较原理和极大值原理进行独立证明。此外，我们还得到了解在边界处的正则性和唯一性的一些结果。本文的结果涵盖了一些重要的模型，如浅水运动的粘性Saint-Venant模型，即θ=1, γ=2。

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引用次数: 0

Well-posedness of the compressible boundary layer equations with analytic initial data 具有解析初始数据的可压缩边界层方程的适定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114110

Ya-Guang Wang , Yi-Lei Zhao

We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic equations and an elliptic equation, describe the behavior of thermal layer and viscous layer in the small viscosity and heat conductivity limit, for the two-dimensional compressible viscous flow with heat conduction with nonslip and zero heat flux boundary conditions. We use the Littlewood-Paley theory to establish the a priori estimates for solutions of this compressible boundary layer problem, and obtain the local existence and uniqueness of the solution in the space of analytic in the tangential variable and Sobolev in the normal variable.

研究了数据在边界切向变量上解析的可压缩边界层方程的适定性。对于二维无滑移零热流边界条件下的热传导可压缩粘性流动，可压缩边界层方程是退化抛物方程和椭圆方程的非线性耦合系统，描述了热层和粘性层在小粘度和导热极限下的行为。利用Littlewood-Paley理论建立了该可压缩边界层问题解的先验估计，得到了该问题解在切向变量和正态变量上的局部存在唯一性。

引用次数: 0

Group noninvariant solutions of the Hénon equation in unbounded domains 无界域hsamnon方程的群非不变解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114113

Ryuji Kajikiya

We study the Hénon equation in unbounded domains Ω which are G invariant, where G is a closed subgroup of the orthogonal group. We say that Ω (or

u (x)

) is G invariant if

g (Ω) = Ω

(or

u (g x) = u (x)

) for any

g \in G

. We call

u (x)

a least energy solution if it is a minimizer of the Rayleigh quotient associated with the Hénon equation. We offer sufficient conditions which guarantee that no least energy solution is G invariant.

研究了无界域Ω上G不变的hsamnon方程，其中G是正交群的闭子群。我们说对于任意G∈G，如果G （Ω）=Ω(或u（gx)=u(x)） Ω（或u(x)）是G不变量。我们称u(x)为最小能量解，如果它是与hsamnon方程相关的瑞利商的最小解。给出了保证没有最小能量解是G不变的充分条件。

引用次数: 0

Directional Poincaré inequality on compact Lie groups 紧李群上的方向poincarcarr不等式

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-15 DOI: 10.1016/j.jde.2026.114109

Paulo L. Dattori da Silva, André Pedroso Kowacs

We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in (2016) [1], to the setting of compact Lie groups. We provide necessary and sufficient conditions for the existence of such an inequality based on estimates on the eigenvalues of the global symbol of the corresponding vector field. We also prove that such refinement of the Poincaré inequality holds for a left-invariant vector field on a compact Lie group G if and only if the vector field is globally solvable, and extend this equivalence to tube-type vector fields on

T^{1} \times G

我们将Steinerberger在（2016）[1]中引入的环面上的定向poincar不等式推广到紧李群的设置中。基于相应向量场的整体符号的特征值估计，给出了该不等式存在的充分必要条件。我们还证明了对紧李群G上的左不变向量场的这种改进当且仅当该向量场是全局可解的，并将此等价推广到T1×G上的管型向量场。

引用次数: 0

Critical blow-up curve in a quasilinear two-species chemotaxis system with two chemicals 具有两种化学物质的拟线性两种趋化系统的临界爆破曲线

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-14 DOI: 10.1016/j.jde.2025.114081

Ziyue Zeng, Yuxiang Li

<div><div>This paper investigates the quasilinear two-species chemotaxis system with two chemicals<span><span><span>(⋆)</span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>∇</mi><mo>⋅</mo><mrow><mo>(</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><mi>w</mi><mo>,</mo><mspace></mspace><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><msub><mrow><mo>⨏</mo></mrow><mrow><mi>Ω</mi></mrow></msub><mi>w</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>∇</mi><mo>⋅</mo><mrow><mo>(</mo><mi>g</mi><mo>(</mo><mi>w</mi><mo>)</mo><mi>∇</mi><mi>z</mi><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>z</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mi>u</mi><mo>,</mo><mspace></mspace><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mo>⨏</mo></mrow><mrow><mi>Ω</mi></mrow></msub><mi>u</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>v</mi></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>w</mi></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>z</mi></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mo>∂</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>w</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> <span><math><mo>(</mo><mi>n</mi><mo>⩾</mo><mn>3</mn><mo>)</mo></math></span> is a smoothly bounded domain. The sensitivity functi

探讨趋化性生态拟线性系统的两种化学物质(⋆){ut =Δu−∇⋅(f (u)∇v), x∈Ω,t> 0, 0 =Δv−μ2 + w,μ2 =⨏Ωw x∈Ω,t> 0, wt =Δw−∇⋅(g (w)∇z), x∈Ω,t> 0, 0 =Δz−μ1 + u,μ1 =⨏Ωu, x∈Ω,t> 0,∂u∂ν=∂v∂ν=∂w∂ν=∂z∂ν= 0,x∈∂Ω,t> 0, u (x, 0) =情况(x) w (x, 0) = w0 (x), x∈Ω,哪里Ω⊂Rn (n⩾3)是一个顺利有限域。灵敏度函数f(s)和g(s)具有以下形式：f(s)≃spg (s)对于s大于或等于1，≃sq,p,q>0。证明了曲线p+q - 4n=max ((p - 2n)q,(q - 2n)p}在（0,4n）×（0,4n）的平方中是（百科）解爆破的临界曲线。更准确地说，•当Ω是一个球时，如果p小于4n，或q小于4n，或0<；p,q<；4n和p+q−4n>；max ((p−2n)q,(q−2n)p}，存在径向对称的初始数据，使得系统（-）承认在有限时间内爆炸的解；•当Ω是光滑有界域时，如果0<；p,q<；4n和p+q−4n<；max ((p−2n)q,(q−2n)p}，对于所有合适的正则初始数据，（-）的对应解是全局有界的。

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