Acta Applicandae Mathematicae最新文献

This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.

In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time.

This paper is dedicated to studying the steady state problem of a population-toxicant model with negative toxicant-taxis, subject to homogeneous Neumann boundary conditions. The model captures the phenomenon in which the population migrates away from regions with high toxicant density towards areas with lower toxicant concentration. This paper establishes sufficient conditions for the non-existence and existence of non-constant positive steady state solutions. The results indicate that in the case of a small toxicant input rate, a strong toxicant-taxis mechanism promotes population persistence and engenders spatially heterogeneous coexistence (see, Theorem 2.3). Moreover, when the toxicant input rate is relatively high, the results unequivocally demonstrate that the combination of a strong toxicant-taxis mechanism and a high natural growth rate of the population fosters population persistence, which is also characterized by spatial heterogeneity (see, Theorem 2.4).

We deal with the following predator-prey model involving nonlinear indirect chemotaxis mechanism

under homogeneous Neumann boundary conditions in a bounded and smooth domain (Omega subset mathbb{R}^{n}) ((ngeq 1)), where the parameters (xi ,chi ,a_{1},a_{2},b_{1},b_{2},alpha ,beta ,gamma >0). It has been shown that if (r_{1}>1), (r_{2}>2) and (gamma (alpha +beta )<frac{2}{n}), then there exist some suitable initial data such that the system has a global classical solution ((u,v,w,z)), which is bounded in (Omega times (0,infty )). Compared to the previous contributions, in this work, the boundedness criteria are only determined by the power exponents (r_{1}), (r_{2}), (alpha ), (beta ), (gamma ) and spatial dimension (n) instead of the coefficients of the system and the sizes of initial data.

We consider in this paper numerical approximation and simulation of a two-species Keller-Segel model. The model enjoys an energy dissipation law, mass conservation and bound or positivity preserving for the population density of two species. We construct a class of very efficient numerical schemes based on the generalized scalar auxiliary variable with relaxation which preserve unconditionally the essential properties of the model at the discrete level. We conduct a sequence of numerical tests to validate the properties of these schemes, and to study the blow-up phenomena of the model in a three-dimensional domain in parabolic-elliptic form and parabolic-parabolic form.

In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of (L_{t}^{infty }L_{x}^{q}) of the density, where (1< q<infty ), and it is independent on the velocity of rotation of the microscopic particles.

The present study investigates an algorithm numerically for finding the solution of partial differential equation with differences involved singular perturbation parameter(SPPDE) on non-uniform grid. Taylor series expansion provides a close approximation of the delay and advance terms in the convection-diffusion terms. After the approximations in shift containing terms, we applied the Crank-Nicolson application on uniform grid in the vertical direction. Subsequently, the resultant system is employed by the method of tension spline on a piece-wise uniform grid. Empirical evidence has shown that the suggested approach exhibits second-order characteristics in both the spatial and temporal dimensions. The effectiveness of derived scheme demonstrated through the solution of examples and the results are compared with existed methods. In the conclusion section, we will discuss the effect of shift parameters behavior for various singular perturbation parameter.

The global dynamics of the typical age-structured model with age-dependent mortality and diffusion rates on unbounded domains have been established. On the one hand, we showed that a positive and constant state solution of the mature population is globally asymptotically stable with respect to the compact-open topology; on the other hand, we showed that the trivial solution is globally asymptotically stable with respect to the usual supremum norm. As an application of our result, we applied the result to birth functions appearing in biology. In addition to the theoretical results, we also present a numerical simulation.

Some global error bounds with undetermined parameters, which are not always valid, for the extended vertical linear complementarity problems (LCP) of CKV-type matrices and CKV-type (B)-matrices, are presented by Yan and Wang (Jpn. J. Ind. Appl. Math. 41:129–150, 2024). In this paper, new global error bounds for the extended vertical LCP of CKV-type matrices and CKV-type (B)-matrices are given, which depend only on the entries of the involved matrices. Numerical examples show that the new bounds are better than those provided in Zhang et al. (Comput. Optim. Appl. 42(3):335–352, 2009) and Wang et al. (Comput. Appl. Math. 40:148, 2021) in some cases.

This article considers the no-flux attraction-repulsion chemotaxis model

defined in a smooth and bounded domain (Omega subset mathbb{R}^{n}) ((nge 2)) with (m_{1},m_{2},m_{3}in mathbb{R}), (chi ,xi ,beta ,delta >0). The functions (f(u)), (g(u)) extend the prototypes (f(u)=alpha u^{s}) and (g(u)=gamma u^{r}) with (alpha ,gamma >0) and suitable (s,r>0) for all (uge 0). Our main result exhibits that there exists (M^{*}>0) such that for all properly regular initial data, the studied model admits a unique classical solution which remains bounded if (m_{2}+s< m_{3}+r) or (m_{2}+s=m_{3}+r) and (frac{xi gamma }{chi alpha }>M^{*}).