Zeitschrift für angewandte Mathematik und Physik最新文献

This paper deals with the following indirect chemotaxis-consumption model with signal-dependent degenerate diffusion and logistic source

under homogeneous Neumann boundary conditions in a smooth bounded domain (Omega subset mathbb {R}^n) ((nge 1)). Here, the parameters (a>0), (b>0), (alpha ge 1), (delta >0) and (l ge 2). For all suitably regular initial data, if one of the following cases holds:

1. (i)

   (l > 2);

2. (ii)

   (l =2, nle 3);

3. (iii)

   (l = 2, n ge 4,) and b is sufficiently large, then the corresponding initial boundary value problem possesses a global classical solution.

In this paper, we deal with an inverse boundary value problem for the Maxwell equations with boundary data assumed known only in accessible part (Gamma ) of the boundary. We aim to prove uniqueness results using the Dirichlet to Neumann data with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index ({{varvec{n}}}) in the interior of a body. Further, using the impedance map restricted to (Gamma ), we may identify locations of small volume fraction perturbations of the refractive index.

The chemotaxis system

is considered under homogeneous Neumann boundary conditions in smoothly bounded domain (Omega subseteq mathbb {R}^n), (nge 2), with constants (0<epsilon <1), (0<chi <1-epsilon ). It is asserted that the problem possesses a uniquely global classical solution whenever the numbers (alpha , beta ) satisfy (1<alpha <2), (beta >frac{n}{2}+alpha -1) or (alpha ge 2), (beta >frac{n}{2}(alpha -1)+1). Moreover, it is shown that if (1<alpha <2), (beta >max {frac{n}{2}+alpha -1, frac{(alpha -1)(1-epsilon )}{(2-alpha )chi }+1}) and (gamma >0) is sufficiently large, then the global-in-time solution is uniformly bounded. In addition, we get similar results for the case of (n=1), which is worth mentioning that the requirement for (epsilon ) and (chi ) is very weak in the global existence result.

The stiffness matrix of a structural Sierpiński triangle under conditions of transversal bending is presented. The derivation is based exclusively on considerations of symmetry, equilibrium, and self-similarity. As a result, the stiffness matrix is shown to depend on a single material parameter. An illustrative numerical example is presented on the basis of an ad hoc computer code for the assembled stiffness of an overall structure consisting of a grid of fractal elements.

This paper is devoted to the asymptotic stability of diverging traveling waves for reaction–advection–diffusion equation (u_{t}-Delta u+alpha (t,y)u_{x}=f(t,y,u)) in cylinders. By the sliding method, we first establish a Liouville-type result. Then, using the Liouville-type result and truncation technique, we prove the asymptotic stability of the diverging traveling wave.

In this paper, we study the following Kirchhoff-type problem with critical nonlinearity

where (Omega ) is a smooth bounded domain in (mathbb {R}^3), (a>0) is a constant, (b,lambda ) are positive parameters and (2<p<4). Under different assumptions on the nonlinearity, the equation has been extensively considered in the case (4<p<6). By contrast, there is no existence result of solutions for the case (2<p<4) since the appearance of the nonlocal term. By using some innovative analytical skills, we obtain the existence results about the sign-changing solutions of this problem. Furthermore, we also present asymptotic behaviors of the sign-changing solutions as (bsearrow 0) or (lambda searrow 0).

This paper considers the wave propagation for a spatial discrete virus model with HIV viral load and 2-LTR dynamics during high active antiretroviral therapy. Applying Schauder fixed point theorem, technique of Lyapunov function and limiting arguments, we establish the existence of traveling wave solutions for the virus model when the basic reproduction number is larger than one and the wave speed is not less than a threshold speed. Then, using the methods of comparison principle and Laplace transform, we prove the nonexistence of traveling wave solutions when the basic reproduction number is either smaller than one; or larger than one but the wave speeds are less than the threshold speed. Indeed, the threshold speed is minimum wave speed for the propagation of traveling waves. We further show that the three classes of inhibitor can decrease the minimum wave speed; while the diffusion rate of visions will increase the minimum wave speed.

We consider a hole embedded in an elastic solid under plane deformation. The solid undergoes a uniform far-field loading while the boundary of the hole is subjected to a uniform pressure. We revisit the design of a harmonic hole such that the mean stress in the entire solid remains constant. We additionally incorporate the change in the direction of the pressure inside the hole in determining the harmonic shape of the hole in case the deformation around the hole is relatively large. We show that the harmonic shape of the hole remains elliptical but its aspect ratio is different from that predicted by the classical solution. We discuss via several numerical examples the differences between the current modified harmonic shape and the classical counterpart as well as how the directional change of the internal pressure influences the aspect ratio of the elliptical harmonic hole within a soft elastic solid.