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In this paper, we study the well-posedness for a class of semilinear superdiffusion equations with spatial nonlocal operators. We first establish the Gagliardo–Nirenberg inequality in ψ -Bessel potential spaces. Based on this, the well-posedness results of local and global mild solution for corresponding linear problem are obtained via apriori estimates. We also obtain the well-posedness results for the nonlinear problem under different conditions. These conclusions are mainly based on the Mihlin–Hörmander’s multiplier estimates, embedding theorem and fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of backward problems for nonlinear fractional super-diffusion equations in Banach spaces. We consider the time fractional derivative in the sense of Caputo type. First, we establish some results for the existence of the mild solutions. Moreover, we obtain regularity results of the first order and fractional derivatives of mild solutions. These conclusions are mainly based on fixed point theorems and properties of α -resolvent family as well as Mittag-Leffler functions. Finally, two applications are provided to illustrate the efficiency of our results. [ABSTRACT FROM AUTHOR]

Distributed-order calculus can summarize the intrinsic multiscale effects of integer and fractional order operators, and construct a more complex physical model. The paper is devoted to study the time distributed-order wave equation. First, we give the definition of distributed-order integral operators I (μ) in α ∈ [ 1 , 2 ] , and from the definition of the integral operator, we found that the operator has similar properties to the fractional integral operators. Next, according to the properties of the distributed-order integral operator and Laplace transform, we obtain the expression of the solution of the distributed-order wave equation. Then we use the resolvent operator to estimate the solution operators. At last, we further studied the liner or semilinear wave problem with the distributed-order derivative on R N and used the contraction mapping principle to prove the existence and uniqueness of mild solution. [ABSTRACT FROM AUTHOR]

This paper addresses the existence and uniqueness of mild solution for fractional Navier–Stokes equation in the homogeneous Besov spaces. The existence and uniqueness of the global mild solution with small initial data is established. The results on existence and uniqueness of the local mild solution for arbitrary initial data are also studied. Meanwhile, we obtain properties about the regularity and decay of mild solutions. These conclusions are mainly based on the fixed point theorems, the implicit function theorem on Banach spaces and the properties of Mittag–Leffler functions. [ABSTRACT FROM AUTHOR]

The microstructure and shear property of Cu/Sn–xZn/Cu (x = 0, 2, 5, 9, 30, 70 wt.%) composite solder joints fabricated by transient liquid phase (TLP) bonding were investigated. The results showed that the appropriate amount of Zn particles inhibited Cu6(Sn, Zn)5 phase formation at the Cu/solder interface. The Zn particles can improve the interface IMC morphology of composite solder joints, the interface IMC thickness of Cu/Sn–30Zn/Cu solder joint is only 3.89 μm, and the excessive (30–70 wt.%) Zn particles are harmful to the composite solder joints. Doping 2–9 wt.% Zn particles can improve the shear strength. The maximum shear strength value of the Cu/Sn–9Zn/Cu composite solder joint reaches 14.18 MPa. The fracture mechanism is mainly ductile brittle mixed fracture, which occurs near the Interface reaction zone. [ABSTRACT FROM AUTHOR]

A two-dimensional phononic crystal sensor model with high-quality factor and excellent sensitivity for sensing acetone solutions and operating at 25–45 kHz is proposed. The model for filling solution cavities is based on reference designs of quasi-crystal and gradient cavity structures. The transmission spectrum of sensor is simulated by the finite element method. High-quality factor of 45,793.06 and sensitivity of 80,166.67 Hz are obtained for the acetone concentration with 1–9.1%, and quality factor of 61,438.09 and sensitivity of 24,400.00 Hz are obtained for the acetone concentration range of 10–100%, which indicated the sensor could still achieve high sensitivity and quality factor at operating frequencies from 25 to 45 kHz. To verify the application of the sensor to sensing other solutions, the sensitivity for sound velocity and density is calculated as 24.61 m-1 and 0.7764 m3/(kg × s), respectively. It indicates the sensor is sensitive to acoustic impedance changes of the solution and equally suitable for sensing other solutions. The simulation results reveal the phononic crystal sensor possessed high-performance in composition capture in pharmaceutical production and petrochemical industry, which can provide theoretical reference for the design of new biochemical sensors for reliable detection of solution concentration. [ABSTRACT FROM AUTHOR]

This paper considers the existence, uniqueness and the asymptotic behavior of a classic heat equation coupled with a fractional ordinary differential system. By the Lumer-Phillips theorem, we obtain the existence and uniqueness of the solution. Furthermore, we use a new Lyapunov functional to show the global attractivity for the considered system, then the tractable global attractive conditions are obtained. Finally, numerical examples are provided to illustrate the applications of our results. [ABSTRACT FROM AUTHOR]

With the rapid development of modern agriculture, non-point source nitrogen pollution from higher polluting farms has become one of the main contributions to the eutrophication of the watershed. This paper first constructed a tripartite evolutionary game model concerning local governments, higher polluting farms, and consumers, all of which participate in the reduction of nitrogen pollution in the river basin. Secondly, the evolution process of evolutionary stability strategy (ESS) and the impact of critical parameters on the strategies of the three stakeholders were analyzed through numerical simulation. The results demonstrated that (1) six ESSs of the system are determined, only (1, 0, 1) is regarded as the most ideal ESS: regulation by local governments, higher polluting farms adopting not purchasing emission rights, and consumers purchasing green agricultural products. (2) The regulation strategy of local governments depends on comparing political losses with the sum of emission reduction subsidies and the supervision cost. (3) The marginal abatement costs, the price of nitrogen emission permits, nitrogen use efficiency, and the subsidy standard for unit emission reduction are the main factors that affect the ESS of higher polluting farms. (4) The ESS of consumers is significantly affected by low-nitrogen preference, government subsidies, and nitrogen use efficiency. This study suggests that the government should strengthen the supervision of the watershed environment from the aspects of improving the market mechanism of nitrogen trading, establishing a dynamic monitoring system, and innovating a subsidy mechanism. [ABSTRACT FROM AUTHOR]

This paper addresses some results about mild solution to time-fractional Navier–Stokes equations with bounded delay existed in the convective term and the external force. Based on the Schauder's fixed point theorem, we establish the sufficient conditions for the existence and uniqueness of the global mild solution in Banach spaces. Moreover, the polynomial decay estimate of the mild solution is given. Furthermore, the approximate controllability for the mild solution is obtained by constructing a Cauchy sequence. [ABSTRACT FROM AUTHOR]

In view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments. [ABSTRACT FROM AUTHOR]