Acta Mathematica Scientia最新文献

Abstract

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

Abstract

This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus (HBV) propagation in an environment characterized by variability and stochas-ticity. Based on some biological features of the virus and the assumptions, the corresponding deterministic model is formulated, which takes into consideration the effect of vaccination. This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations. The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps. By developing the assumptions and employing the novel theoretical tools, the threshold parameter responsible for ergodicity (persistence) and extinction is provided. The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed. Moreover, we obtain the following new interesting findings: (a) in each class, the average time depends on the value of α; (b) the second-order noise has an inverse effect on the spread of the virus; (c) the shapes of population densities at stationary level quickly changes at certain values of α. The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.

Abstract

In this paper, we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property. We introduce the concepts of the weak*-weak denting point and the weak*-weak* denting point of a set. These are the generalizations of the weak* denting point of a set in a dual Banach space. By use of the weak*-weak denting point, we characterize the very smooth space, the point of weak*-weak continuity, and the extreme point of a unit ball in a dual Banach space. Meanwhile, we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces. Moreover, we define the nearly weak dentability in Banach spaces, which is a generalization of near dentability. We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability. We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

Abstract

Assume that L is a non-negative self-adjoint operator on L²(ℝⁿ) with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space on ℝⁿ satisfying some mild assumptions. Let H_{X, L}(ℝⁿ) be the Hardy space associated with both X and L, which is defined by the Lusin area function related to the semigroup generated by L. In this article, the authors establish various maximal function characterizations of the Hardy space H_X,L(ℝⁿ) and then apply these characterizations to obtain the solvability of the related Cauchy problem. These results have a wide range of generality and, in particular, the specific spaces X to which these results can be applied include the weighted space, the variable space, the mixed-norm space, the Orlicz space, the Orlicz-slice space, and the Morrey space. Moreover, the obtained maximal function characterizations of the mixed-norm Hardy space, the Orlicz-slice Hardy space, and the Morrey-Hardy space associated with L are completely new.

Abstract

This paper is a continuation of recent work by Guo-Xiang-Zheng [10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation $$Delta^{2}u=Delta(Vnabla u)+{text{div}}(wnabla u)+(nablaomega+F)cdotnabla u+fqquadtext{in}B^{4},$$ under the smallest regularity assumptions of V, ω, ω, F, where f belongs to some Morrey spaces. This work was motivated by many geometrical problems such as the flow of biharmonic mappings. Our results deepens the L^p type regularity theory of [10], and generalizes the work of Du, Kang and Wang [4] on a second order problem to our fourth order problems.

Abstract

In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

Abstract

In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ Mⁿ in the Lorentz manifold Mⁿ × ℝ with the metric −ds² + σ, where Mⁿ is a complete Riemannian n-manifold with the metric σ, Ω has piecewise smooth boundary, and ℝ denotes the Euclidean 1-space. We prove an interesting stability result for translating spacelike graphs in Mⁿ × ℝ under a conformal transformation.

This paper deals with the radial symmetry of positive solutions to the nonlocal problem

where b: B₁ → ℝ is locally Holder continuous, radially symmetric and decreasing in the ∣x∣ direction, f: ℝ → ℝ is a Lipschitz function, h: B₁ → ℝ is radially symmetric, decreasing with respect to ∣x∣ in ℝ^NB₁, B₁ is the unit ball centered at the origin, and (( - Delta )_gamma ^s) is the weighted fractional Laplacian with s ∈ (0, 1), γ ∈ [0, 2s) defined by

We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space

under suitable additional assumptions on b and f. Our symmetry results are derived by the method of moving planes, where the main difficulty comes from the weighted fractional Laplacian. Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators

under suitable additional assumptions on b, f and h.

In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J Differ Equ, 2021, 302: 807–853] studied the persistence or extinction of the prey and of the predator separately in various moving frames. In particular, they achieved a complete picture in the local diffusion case. However, the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.’s paper. By using some a prior estimates, the Arzelà-Ascoli theorem and a diagonal extraction process, we can extend and improve the main results of Choi et al. to achieve a complete picture in the nonlocal diffusion case.

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source

The system here is under a homogenous Neumann boundary condition in a bounded domain Ω ⊂ ℝⁿ(n ≥ 2), with χ, ξ, α, β, γ, δ, k₁, k₂ > 0, p ≥ 2. In addition, the function f is smooth and satisfies that f(s) ≤ κ − μs^l for all s ≥ 0, with κ ∈ ℝ, μ > 0, l > 1. It is shown that (i) if (l>max{2k_{1},{2k_{1}nover{2+n}}+{1over{p-1}}}), then system possesses a global bounded weak solution and (ii) if (k_{2}>max{2k_{1}-1,{2k_{1}nover{2+n}}+{2-pover{p-1}}}) with l > 2, then system possesses a global bounded weak solution.