Acta Applicandae Mathematicae最新文献

In this work, the local decomposition of pressure in the Navier-Stokes equations is dynamically refined to prove that a relevant critical energy of a Leray-type solution inside a backward paraboloid—regardless of its aperture—is controlled near the vertex by a critical behavior confined to a neighborhood of the paraboloid’s boundary. This neighborhood excludes the interior near the vertex and remains separated from the temporal profile of the vertex, except at the vertex itself. Moreover, we present a refined scaling-invariant regularity result.

Existing literature shows that the vacuum stability of a general scalar potential is equivalent to the strict copositivity of its corresponding coupling tensor. In order to judge the copositivity of a coupling tensor, we provide two criteria of a strict copositive tensor, and show their correctness and effectiveness via two practical examples by checking the vacuum stability of a general scalar potential for (mathbb{Z}_{3}) scalar dark matter.

In this paper, we consider the following consumption chemotaxis system

under the smooth bounded domain (Omega subset mathbb{R}^{n},,(nge 2)) with homogeneous Neumann boundary conditions, where the parameters (a>0), (b>0), (gamma ge 2) and (delta >0). It has been shown that for any sufficiently regular initial data, the associated initial-boundary value problem has a global classical solutions.

To have proper multiscale simulations by central high-resolution schemes, the performance of slope limiters is crucial on adapted cells in terms of stability, accuracy, high-resolution, entropy-satisfying and spectral features. Hence, here, different families of slope limiters are extended or developed over non-uniform centered/non-centered cells, obtained by the wavelet-based adapted grids. The developed limiters on adaptive cells, are: (1) The entropy-satisfying limiter, (2) Second-order non-symmetric limited slopes and corresponding symmetric formulations, (3) Limiters with symmetric three-point stencils, second-order accuracy and the total variation diminishing (TVD) feature. The three-point stencil slope limiters do not preserve the symmetry feature on non-uniform cells. However, slopes obtained by non-symmetric stencils nearly preserve the symmetric property for different directions, as the direction-effect is inherent in their formulations. For non-symmetric limiters, firstly, corresponding TVD and monotonicity-preserving conditions are provided. Then, eight non-symmetric limited slopes are developed with four-, five- and three-point stencils. They are then unified to achieve four symmetric limiters. For the symmetric limiters with three-point stencils, also, the concept of blending of two limiters is updated to achieve compression-adaptive limiters. All limiters are used in the cell-adaptive Kurganov-Tadmor (KT) central scheme. Afterwards, the effects of limited slopes are studied on spectral properties. Finally, several problems are presented.

Extremum problems with vanishing constraints are models several applications in structural and topology optimization. In this paper, a class of nonsmooth vector optimization problems with both inequality, equality and vanishing constraints is considered. The Abadie regularity condition and the modified Abadie regularity condition are introduced for the aforesaid multicriteria optimization problems if the functions constituting them are Hadamard differentiable. Under the mentioned regularity conditions, the Karush-Kuhn-Tucker type necessary optimality conditions are established for vector optimization problems with vanishing constraints in which the involved functions are Gàteaux differentiable. Further, the sufficient optimality conditions are proved for such nondifferentiable multiobjective programming problems with vanishing constraints under assumptions that the objective functions are pseudo-convex and constraint functions are quasi-convex. Thus, the fundamental results from optimization theory, that is, optimality conditions are proved for a new class of structural and topological optimization problems for which the aforesaid multicriteria optimization problems with vanishing constraints are models.

This study examines whether a traveling wave solution for an addiction reaction-diffusion epidemic model with dispersed delays exists or not. The primary characteristic of the model is the potential weakness in the standard comparison principle, which prevents many known conclusions from being applied. If the basic reproduction number of the model, indicated by (R_{0}), is larger than one, there is a minimal wave speed, denoted by (c^{*}>0), such that the system admits a nontrivial traveling wave solution with wave speed (c) when (cgeq c^{*}). However, for either (R_{0}>1) and (c< c^{*}), or (R_{0}<1), there is no nontrivial traveling wave solution.

In this paper, we consider a degenerate/singular wave equation that is fixed at the point where the degeneracy occurs and stabilized with a time-delayed boundary feedback at the other endpoint. First, we study the well-posedness of the system under consideration in appropriate weighted spaces by using semigroup theory. Then, we prove its exponential stability under a suitable condition on both coefficients of the delayed damping term and the not delayed one. Furthermore, an explicit expression of the exponential decay in terms of the system parameters is provided, leveraging both the multiplier method and the Lyapunov functional approach.

Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the feature of complex scalar terms. We delineate on the crucial role of these extended definition of quaternions in formulating Maxwell equations, having properly defined a pure quaternion containing the components of the classical electric and magnetic fields. Through a formal introduction, we describe the approach followed to acquiring time-like quaternions, characterized by having complex scalar term, and their significant relationship with the derivation of Maxwell equations. This topic not only underscores the mathematical intricacies of quaternionic algebra, but also highlights its profound implications in the description of fundamental electromagnetic phenomena.

In this paper, we are concerned about the steady state problem of a degenerate predator-prey model with cross-diffusion. First, some properties of principal eigenvalues are deduced. Next, the stability of the semitrivial steady state solutions are obtained. Finally, existence, uniqueness and stability of positive steady state solutions are derived. The result reveals that the diffusion with spatial degeneracy profoundly influences the structure and stability of semitrivial steady state solutions and the coexistence region, which is a strong contrast to the result with no spatial degeneracy.

This paper deals with a two-dimensional Keller-Segel-Navier-Stokes system of coral fertilization with porous medium diffusion. When the nonlinear diffusion exponents of sperms and eggs (m>frac{1}{2}), (l>0) respectively, as well as the strength of fertilization (mu >0), the system possesses a global bounded weak solution. Furthermore, if (0< l<1), the corresponding global weak solution stabilizes to the spatially homogeneous equilibrium ((n_{infty },rho _{infty },rho _{infty },0)) in an appropriate sense, where (n_{infty }:=frac{1}{|Omega |}(int _{Omega }n_{0}-int _{Omega } rho _{0})_{+}) and (rho _{infty }:=frac{1}{|Omega |}(int _{Omega }rho _{0}-int _{ Omega }n_{0})_{+}).