Zeitschrift für angewandte Mathematik und Physik最新文献

The (3times 3) blood flow dynamic model describes the flow of blood in flexible vessels. We study the inviscous blood flow in arteries model in this paper. The elementary waves of the blood flow in arteries include the rarefaction wave, the shock wave and the stationary wave which appears where the material properties of vessel wall change. The interactions of stationary wave with rarefaction wave and shock wave in arteries are discussed in detail. We focus on the changes of the cross-sectional area of the blood vessel and the averaged axial velocity of blood flow after the rarefaction wave and the shock wave penetrate the stationary wave. They change after interactions.

We consider the following Kirchhoff equation in the Sobolev critical case with combined power nonlinearities

having prescribed mass

where (a, c, mu >0) are positive constants, (b>0) is a positive parameter, (2<q<{bar{p}}:=2+frac{8}{3}) which is (L^{2})-critical exponent. For the (L^{2})-subcritical case (2<q<frac{10}{3}) and Sobolev critical case, Li et al. (2021) proved that (({mathcal {K}})) has a solution which is ground state solution and corresponds to local minima of the associated energy functional. Here we extend the result in Li et al. (2021) by proving that (({mathcal {K}})) has the second solution which is not a ground state and is located at a mountain-pass level of the energy functional. Meanwhile, let (u_{b}) are normalized solutions of mountain-pass type to (({mathcal {K}})), then (u_{b}rightarrow u) in (H^{1}({mathbb {R}}^{3})) as (brightarrow 0) up to a subsequence, where (uin H^{1}({mathbb {R}}^{3})) is a normalized solution of mountain-pass type to

Our results also extend the results of Soave (J Differ Equ 269:6941–6987, 2020; J Funct Anal 279:108610, 2020).

In this paper, we introduce a new vectorized MATLAB-based algorithm for efficient serial computation of global matrix/force arising from finite element method (FEM) for meshes of any type and approximation order in linear elasticity. Because for-loops in MATLAB are very slow, we propose a modified process that takes advantage of vectorization and sparse assembly to achieve good performance while using the same memory as the standard algorithm. For this purpose, by using good programming practices, the implementation of this scheme is succinctly described and can be integrated into any MATLAB package dealing with FEM. Specifically, attention is paid to the calculation of the triplet (row index, column index, matrix components) as well as the assembly of the global stiffness matrix, mass matrix and force vector. Additionally, an extension of the proposed approach for Mindlin plate theory and functionally graded materials is outlined. Finally, the accuracy of this strategy is verified on selected numerical tests after comparing the obtained results with those of ABAQUS. In terms of performance, the study conducted on a set of meshes considering the standard algorithm and two other well-known MATLAB vectorized algorithms revealed that: (i) for a 2D beam problem meshed with (P_{1})-triangle elements, a speedup of about 8 and 15 is achieved with sparse and fsparse, respectively. (ii) for a 3D plate problem meshed with (P_{1})-tetrahedral elements, a speedup of about 4 and 8 is achieved with sparse and fsparse, respectively. When compared to ABAQUS performance, the proposed scheme results in a computational time that is about five times smaller.

This article focuses on the analytical investigation of strain-induced ultrafast magnetic domain wall motion in a bilayer structure composed of piezoelectric and magnetostrictive materials. We perform the analysis within the framework of the inertial Landau–Lifshitz–Gilbert equation, which describes the evolution of magnetization in cubic magnetostrictive materials. By employing the classical traveling wave ansatz, the study explores how various factors such as magnetoelasticity, dry-friction, inertial damping, chemical composition, crystal symmetry, and tunable external magnetic field influence the motion of the domain walls in both steady-state and precessional dynamic regimes. The results provide valuable insights into how these key parameters can effectively modulate dynamic features such as domain wall width, threshold, Walker breakdown, and domain wall velocity. The obtained analytical results are further numerically illustrated, and a qualitative comparison with recent observations is also presented.

In this paper, we investigate a strong form of propagation of chaos for Cucker–Smale model. We obtain an explicit bound on the relative entropy in terms of the number of particles between the joint law and the tensioned law of particles, which implies the mean field limit of the Cucker–Smale model and the propagation of chaos through the strong convergence of all marginals. Our method relies mainly on the new law of large numbers for Jabin and Wang (Invent Math 214:523–591, 2018) at the exponential scale.

In this paper, we study an initial-boundary value problem of the doubly dispersive quasilinear wave equation

where (Omega ) is an open bounded domain in ({mathbb {R}}^{n}) with smooth boundary; (T_{max }(le +infty )) denotes the maximal existence time; (p,q>2) are constants. We denote (q=p) the critical exponent for blow-up solutions. For (q<p), we prove that all the weak solutions are globally bounded even if the initial energy is negative. For (qge p), we obtain the optimal classification of initial data on the existence of global and blow-up solutions, which is divided into the subcritical, critical, and super critical initial energy in the framework of potential well. By constructing new auxiliary functions, we obtain the upper bounds of blow-up time for different norms.

The present paper is devoted to the study of the following double-phase equation

where (Nge 2), (1<p<q<N), (q<p^{*}) with (p^{*}=frac{Np}{N-p}), (mu :mathbb {R}^{N}rightarrow mathbb {R}) is a continuous non-negative function, (mu _{varepsilon }(x)=mu (varepsilon x)), (V:mathbb {R}^{N}rightarrow mathbb {R}) is a positive potential satisfying a local minimum condition, (V_{{{,mathrm{varepsilon },}}}(x)=V({{,mathrm{varepsilon },}}x)), and the nonlinearity (f:mathbb {R}rightarrow mathbb {R}) is a continuous function with subcritical growth. Under natural assumptions on (mu ), V and f, by using penalization methods and Lusternik–Schnirelmann theory we first establish the multiplicity of solutions, and then, we obtain concentration properties of solutions.

The main objective of this paper is to consider a continuous data assimilation algorithm for the three-dimensional planetary geostrophic model in the case that the observable measurements, obtained continuously in time, may be contaminated by systematic errors. In this paper, we will provide some suitable conditions on the nudging parameter and the spatial resolution, which are sufficient to show that the approximation solution of the proposed continuous data assimilation algorithm converges to the unique exact unknown reference solution of the original system at an exponential rate, asymptotically in time, under the assumption that the observed data is free of error.

How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem. We consider a macroscopic road traffic model on networks, semi-discretized in space and decide to give ourselves the possibility to control the flow at junctions. Our target is to smooth the traffic along a given path within a fixed time. A parsimony constraint is imposed on the controls, in order to ensure that the optimal strategies are feasible in practice. We perform an analysis of the resulting optimal control problem, proving the existence of an optimal control and deriving optimality conditions, which we rewrite as a single functional equation. We then use this formulation to derive a new mixed algorithm interpreting it as a mix between two methods: a descent method combined with a fixed point method allowing global perturbations. We verify with numerical experiments the efficiency of this method on examples of graphs, first simple, then more complex. We highlight the efficiency of our approach by comparing it to standard methods. We propose an open source code implementing this approach in the Julia language.

In this paper, we study the possible singular points of suitable weak solutions to the 3D co-rotational Beris-Edwards system. Inspired by the work of He et al. (J. Nonlinear Sci. 29:2681–2698, 2019) and Wang et al. (Nonlinearity 32:4817–4833, 2019) for Navier–Stokes equations, we established a new partial regularity criteria for co-rotational Beris-Edwards system. As an application, we prove the known Minkowski dimension of the potential interior singular set of suitable weak solutions of the co-rotational Beris-Edwards system is (frac{7}{6}(approx 1.167)).