Zeitschrift für angewandte Mathematik und Physik最新文献

This paper studies an impact of media epidemic system with diffusion and linear source. We first derive the uniform bounds of solutions to impact on media reaction diffusion system. Then, the basic reproduction number is calculated and the threshold dynamics of impact media reaction diffusion system is also given and the Kuratowski measure (kappa ) of non-compactness is also considered. In addition, assume the spatial environment is homogeneous, it is shown that the unique endemic equilibrium of the system is global stability by constructing suitable Lyapunov function. Finally, we discuss the asymptotic profile of the system when the diffusion rate of the susceptible (infected) individuals for the system tends to zero or infinity. The main results show that the activities of infected individuals can only be at low risk, and then the virus eventually will be extinct, that is, to control the entry of viruses from abroad and increase the detection of domestic viruses. Finally, some numerical simulations are worked out to confirm the results obtained in this paper.

A recent theoretical study (Xu in Proc R Soc A Math Phys Eng Sci 477:20200913, 2021) has derived conditions on the coefficients of Jeffreys-type equation to predict thermal oscillations and resonance during phonon hydrodynamics in non-metallic solids. Thermal resonance, in which the temperature amplitude attains a maximum value (peak) in response to an external exciting frequency source, is a phenomenon pertinent to the presence of underdamped thermal oscillations and explicit finite speed for the thermal wave propagation. The present work investigates the occurrence condition for thermal resonance phenomenon during the electron–phonon interaction process in metals based on the hyperbolic two-temperature model. First, a sufficient condition for underdamped electron and lattice temperature oscillations is discussed by deriving a critical frequency (a material characteristic). It is shown that the critical frequency of thermal waves near room temperature, during electron–phonon interactions, may be on the order of terahertz ((10-20) THz for Cu and Au, i.e., lying within the terahertz gap). It is found that whenever the natural frequency of metal temperature exceeds this frequency threshold, the temperature oscillations are of underdamped type. However, this condition is not necessary, since there is a small frequency domain, below this threshold, in which the underdamped thermal wave solution is available but not effective. Otherwise, the critical damping and the overdamping conditions of the temperature waves are determined numerically for a sample of pure metals. The thermal resonance conditions in both electron and lattice temperatures are investigated. The occurrence of resonance in both electron and lattice temperature is conditional on violating two distinct critical values of frequencies. When the natural frequency of the system becomes larger than these two critical values, an applied frequency equal to such a natural frequency can drive both electron and lattice temperatures to resonate together with different amplitudes and behaviors. However, the electron temperature resonates earlier than the lattice temperature.

The long-term behavior of low regularity solutions to the damped BBM equation with a distribution force on the torus is studied. Since the energy equation fails to hold for the low regularity solutions, the existence of a bounded absorbing set is not a trivial. This difficulty is overcome by splitting the solution into five parts, where some parts decay exponentially in gradually higher regularity spaces, the final remainder belongs the energy space and thus enjoys the dissipative effect. In this way, the existence of a global attractor is proved in the sharp low regularity space. Moreover, the attractor is shown to have a finite fractal dimension based on the quasi-stable estimate method.

In this paper, we study the Cauchy problem for a system of nonlinear Schrödinger equations with quadratic interactions and initial data belonging to a class of analytic Gevrey functions. Here, we present a local well-posedness result in the analytic Gevrey class (G^{sigma ,s}times G^{sigma ,s}) by proving some bilinear estimates in Bourgain’s space with exponential weight. Furthermore, we prove that the obtained solution can be extended to any time (T>0), as long as the radius of the spatial analyticity (sigma ) is bounded below by (cT^{-2}), if (0<a <1/2), or (cT^{- 4}), if (a>1/2).

In this paper, we study the (Gamma )-limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the (Gamma )-convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with “smooth” solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam.

This study investigates the thermocapillary migration of a compound drop placed concentrically within a spherical cavity under the limit of vanishing Péclet and Reynolds number. The imposed temperature gradient, which is constant along the line connecting the centers of the drop and cavity, is the driving force for the migration of compound drop. The compound drop is assumed to translate with an unknown velocity to be determined using force-free conditions. The flow field in each phase of the drop and the continuous phase is governed by the Stokes equations, whereas the thermal problem in each phase is governed by the heat conduction equation. The hydrodynamic problem and the thermal problem are coupled through specific boundary conditions. A complete general solution of the Stokes equation is used to solve the hydrodynamic problem in each phase. The migration velocity of a compound drop inside a spherical cavity is presented for various values of the physical parameters involved such as viscosity ratio, thermal conductivity ratio, Marangoni number. It has been observed that the migration velocity which represents the rate of movement of compound drop due to thermocapillary effects, decreases as the ratio of the compound drop’s radius to the cavity radius increases. On the other hand, this velocity decreases with an increase in relative conductivity of the cavity wall and increases with Marangoni number at the interface of the compound drop. The analytical solution provides a closed-form expression for the migration velocity of the confined compound drop, and it is seen that the boundary effects play significant role in thermocapilary migration.

The current work investigates the transverse vibration of a piezothermoelastic (PTE) nanobeam in the frame of dual-phase-lag thermoelasticity theory. Closed-form analytical expression for the thermoelastic damping (TED) in terms of quality factor for a homogeneous transversely isotropic PTE beam is derived by using Euler–Bernoulli beam theory and complex frequency approach. The size effect of the nanostructured beam is tackled by applying modified couple stress theory (MCST). Detailed analysis on damping of vibration owing to thermal fluctuations and electric potential in the present context under three sets of boundary conditions is attempted to investigate the influences of two-phase-lag parameters, piezoelectric parameter, thermal effect and size-dependent behaviour on energy dissipation caused by TED in PTE beam resonators. Analytical results are illustrated with the help of graphical plots on numerical findings for lead zirconate titanate (PZT-5A) PTE material. The investigation brings out some significant key findings and observations in view of the present heat conduction model.

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping ((-Delta )^{2theta }v_t) with (theta in [frac{1}{2},1]). By using the semigroup method and the multiplier technique, we obtain the exact polynomial decay rates, and find that the polynomial decay rate of the system is determined by the inertia/elasticity ratios and the fractional damping order. Specifically, when the inertia/elasticity ratios are not equal and (theta in [frac{1}{2},frac{3}{4}]), the polynomial decay rate of the system is (t^{-1/(10-4theta )}). When the inertia/elasticity ratios are not equal and (theta in [frac{3}{4},1]), the polynomial decay rate of the system is (t^{-1/(4+4theta )}). When the inertia/elasticity ratios are equal, the polynomial decay rate of the system is (t^{-1/(4+4theta )}). Furthermore it has been proven that the obtained decay rates are all optimal. The obtained results extend the results of Oquendo and Suárez (Z Angew Math Phys 70(3):88, 2019) for the case of fractional damping exponent (2theta ) from [0, 1] to [1, 2].

In a recent paper Li et al. (Z Angew Math Phys 73:52, 2022. https://doi.org/10.1007/s00033-022-01681-4) have considered a generalized nonlinear Schrödinger equation which has extensive applications in various fields of physics and engineering. After proving Liouville integrability of this equation, they investigated the phenomenon of the modulational instability for the possible reason of the formation of the rogue waves. By means of the generalized ((2,N-2))-fold Darboux transformation, authors presented several mixed localized wave solutions, such as breathers, rogue waves and semi-rational solitons for their model equation, and accurately analyzed a number of important physical quantities. It is the aim of this Comment to point out that (i) the baseband modulation instability was developed in a wrong way and (ii) one of the two different types of Taylor series expansions for solution of Lax pair used in that article for building analytical solutions, especially the one obtained with (xi _{j}=Z) does not correspond to any solution of the spectral problem (2.1) when using ( u_{0}left( x,tright) ) as the seed solution. Consequently, all mixed localized solutions that involve the mentioned Taylor series are invalid.

The aim of this paper is to establish an Ambrosetti–Prodi type result involving Dirac weights

where (delta (x-x_i)) is the canonical Dirac delta function at the point (x_i), (i=1,2,ldots ,p), (pin mathbb {N}), (0=x_0<x_1<cdots<x_p<x_{p+1}=1), (qin C([0,1],[0,+infty ))), (fin L^1([0,1],mathbb {R})), (gin C^{1}(mathbb {R},mathbb {R})), (cin C([0,1],[0,+infty ))), (c_iin [0,+infty )). The main tools used are the sub-super-solution method and Leray–Schauder topological degree theory.