We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of the elementary symmetric functions of the eigenvalues splitting a multiple eigenvalue, as well as a Rellich-Nagy-type result describing the corresponding bifurcation phenomenon. We also address an isoperimetric problem and characterize the critical cavities for the symmetric functions of the eigenvalues subject to isovolumetric or isoperimetric domain perturbations and prove that balls are critical. We include known formulas for the eigenpairs in a ball and calculate the first one.

In this paper, an inverse time-fractional Schr$\ddot{o}$dinger problem of potential-free field is studied. This problem is ill-posed, i.e, the solution (if it exists) does not depend continuously on the data. Based on an a priori bound condition, the optimal error bound analysis is given. Moreover, a modified kernel method is introduced. The convergence error estimate obtained by this method under the priori regularization parameter selection rule is optimal, and the convergence error estimate obtained under the posteriori regularization parameter selection rule is order-optimal. Finally, some numerical examples are given to illustrate the effectiveness and stability of this method.

This paper attempts to focus on the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm which combines the hybrid projection method and the inertial technique. The strong convergence theorems of this algorithm are obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of operator norms. Some numerical experiments in infinite Hilbert space are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existin

An efficient multiscale-like multigrid (MSLMG) method is presented to solve the two-dimensional (2D) convection-diffusion equations on nonuniform grids, based on the transformation-free high order compact (HOC) difference scheme. By providing appropriate initial solutions, the discretization systems on the two finest grids are solved to obtain the MSLMG solutions with discretization-level accuracy by performing few multigrid cycles, which implemented with alternating line Gauss-Seidel smoother, interpolation and restriction on nonuniform grids. Numerical experiments of two boundary layer and local singularity problems are conducted to demonstrate the proposed algorithm is efficient and effective to decrease the computational cost.

As the pandemic of Coronavirus Disease 2019 (COVID-19) rages throughout the world, accurate modeling of the dynamics thereof is essential. However, since the availability and quality of data varies dramatically from region to region, accurate modeling directly from a global perspective is difficult, if not altogether impossible. Nevertheless, via local data collected by certain regions, it is possible to develop accurate local prediction tools, which may be coupled to develop global models. In this study, we analyze the dynamics of local outbreaks of COVID-19 via a coupled system of ordinary differential equations (ODEs). Utilizing the large amount of data available from the ebbing outbreak in Hubei, China as a testbed, we estimate the basic reproductive number, R0 of COVID-19 and predict the total cases, total deaths, and other features of the Hubei outbreak with a high level of accuracy. Through numerical experiments, we observe the effects of quarantine, social distancing, and COVID-19 testing on the dynamics of the outbreak. Using knowledge gleaned from the Hubei outbreak, we apply our model to analyze the dynamics of outbreak in Turkey. We provide forecasts for the peak of the outbreak and the total number of cases/deaths in Turkey, for varying levels of social distancing, quarantine, and COVID-19 testing.

The present paper is devoted to study the space identification problem for the elliptic-telegraph differential equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the space identification problem for the elliptictelegraph differential equation is proved. In applications, theorems on the stability of three source identification problems for one dimensional with nonlocal conditions and multidimensional elliptic-telegraph differential equations are established.

In that paper, firstly we get two additional different non-null space curve evolutions in Minkowski 3-space by considering Landau-Lifshitz (LL-) equation where we identify the spin vector with the binormal vector and the normal vector of these curves, respectively. Then, we obtain some links for constructing the moving non-null space curves by using the integrable LL- equation. Finally, we give as an application, the exact solution of the moving non-null curve evolutions obtained by taking the spin vector the normal vector of the curve and we showed graphically that these solutions are wave solutions.

The paper deals with boundedness problems of  integral operators in weighted grand Bochner-Lebesgue spaces. We will treat both cases: when a weight function appears as a multiplier in the definition of the norm, or when it defines the absolute continuous measure of integration. Along with the diagonal case we deal with the off-diagonal case. To get the appropriate result for the Hardy-Littlewood maximal operator we rely on the reasonable bound of the sharp constant in the Buckley type theorem which is also derived in the paper.

This work deals with intrinsic decay rates for the energy of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. We prove the intrinsic decay rates for the energy of a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition of relaxation kernels described by the inequality g_{i}′(t)≤-H(g_{i}(t)), (i=1,2) for all t≥0, with H convex.

In this paper, we deal with the numerical approximation of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term. Since the equation is a nonlinear equation, the Raviart-Thomas mixed finite element method is one of the most suitable techniques to obtain the approximated solution. In this paper, we will show that using the Raviart-Thomas method the optimal convergence order of the scheme can be achieved. To that end, we prove the necessary lemmas and the main theorem. Finally, the efficiency of the method is certified by numerical examples.

Assuming non-Fourier thermal effects, Tzou's dual-phase-lag model has been applied to introduce the governing heat conduction equation in the presented mathematical model. Moreover, in order to design a well-posed stable dual-phase-lag model, the governing time fractional dual-phase-lag heat equation has been established by introducing conductive temperature and thermodynamical temperature, satisfying the two-temperature theory. Due to the application of phase-lags the heat conduction equation became hyperbolic. The corresponding governing equations of motion and stresses have been considered in two-dimensional bounded spherical domain. The spherical boundaries are assumed to be traction free. The Laplace and the Legendre integral transforms have been applied to obtain the analytical solutions of conductive and thermodynamical temperatures, displacement components and thermal stresses. The Gaver-Stehfest algorithm has been employed to achieve the time domain inversions of Laplace transforms numerically, satisfying the Kuznetsov convergence criteria. Classical, fractional and generalized thermoelasticity theories has been recovered theoretically and numerically as well for various fractional orders and phase-lags values.

How to understand the dynamical collective performances is of particular significance in both theories and applications. In this paper, we are interested in investigating the combined influences of local interaction and processing delay on the asymptotic behaviour in a particle model with local communication weights. As new observations, we show that the desired particle system undergoes both periodic flocking and periodic clustering behaviors when the processing delay crosses a threshold value and the eigenvalue $1$ of average matrix is semi-simple. In this case, the connectedness of the particle system may be absent. Also, the number of clusters is discussed by using the subspace analysis. In results, some criterion of flocking and clustering emergence with exponential convergent rate are established by the standard functional differential equations analysis when the processing delay is small. When the processing delay reaches the threshold value, the system undergoes periodic flocking and periodic clustering emergence. It also shows that the processing time lags qualitatively change the emergent performances in a nonlinear way. Finally, we conclude this study with several numerical simulations that intuitively illustrate the validity of the theoretical results and address some discussions for both variable communication weight and distributed processing delay.

Current study investigates thermal-hydraulic performances of turbulent forced hybrid nanofluid flow and heat transfer inside a parabolic through solar collector equipped with turbulators. The main aim of present work is to simulate and investigate the effects of different Reynolds numbers and geometrical parameters on thermal and hydraulic characteristics of the system to achieve the maximum PEC value. The heat transfer fluid is water-based MWCNT-Al2O3 (80%:20%) hybrid nanofluid which makes a Newtonian nanofluid. The RANS equations with the shear-stress (SST) k–ω turbulence model have been employed for modeling the turbulence regime. Based on obtained results, usage of turbulators leads to higher thermal diffusion because of destroying the laminar sub layer, increasing heat transfer surface and convection heat transfer. For θ=180°, the maximum values of average Nusselt number (Nuave) are achieved during all studied range of Reynolds numbers followed by θ=90° and θ=0°, respectively. For HO=15mm, the maximum values of Nuave are achieved followed by HO=10mm and HO=5mm, respectively. The model with HO=5mm has not the maximum Nuave; but, it has lower pressure drop than HO=15mm. For BO=1000mm, the maximum values of Nuave are achieved followed by BO=800mm and smooth channel, respectively. Furthermore, for δ=60°, the maximum Nuave are achieved followed by δ=40° and δ=20°, respectively. For model δ=40° the maximum values of PEC are achieved followed by smooth channel, δ=20° and δ=60°, respectively. The parabolic through solar collector model with θ=180°, HO=15, BO=1000mm, δ=40° and bO=20mm filled with hybrid nanofluid suggested as the optimum model in the present investigation.

In this paper, we investigate the decay properties of the thermoelastic Timoshenko system with past history in the whole space where the thermal effects are given by Cattaneo and Fourier laws. We obtain that both systems, Timoshenko-Fourier and Timoshenko-Cattaneo, have the same rate of decay (1+t)^{-(1/4)} and the regularity-loss type property is not present in some cases. Moreover, new stability number χ is introduced, such new number controls the decay rate of the solution with respect to the regularity of the initial data. To prove our results, we use the energy method in Fourier space to build an appropriate Lyapunov functionals that give the desired results.

We study the existence of global bounded smooth solutions to the one-dimensional nonisentropic Euler system with large initial data. We find a sufficient condition on the initial data to obtain the existence of global bounded classical solution to the Cauchy problem.

Studying spread of epidemics and diseases are world wide problems especially during the current time where the whole world is suffering from COVID-19 pandemic. Antimicrobial resistance (AMR) and waning vaccination are classified as world wide problems. Both depend on the exposure time to antibiotic and vaccination. Here, a simple model for competition between drug resistant and drug sensitive bacteria is given. Conditions for local stability are investigated which agree with observation. Existence of positive solution in the AMR complex networks is proved. Dynamics of the identical AMR models are explored with different topologies of complex networks such as global, star, line and unidirectional line networks coupled through their susceptible states. Chaotic attractors are shown to be existed as the AMR models are located on all the indicted topologies of complex networks. Thus, it is found that the dynamics of the AMR model become more complicated as it is located on either integer-order or fractional-order complex networks. Furthermore, a discretized version of the fractional AMR model is presented. Complex dynamics such as existence of Neimark–Sacker, flip bifurcations, coexistence of multi attractors, homoclinic connections and multi closed invariant curves are investigated. Basin sets of attraction are also computed. Finally, the discretized system is located on complex networks with different topologies which also show rich variety of complex dynamics. Also, 0-1 test is used to verify the existence of unpredictable dynamics. So, studying the dynamics of AMR models on complex networks is very helpful to understand the mechanism of spread of diseases.

In this paper, we investigate the surface-dependent growth model in Euclidean 3-space. The surface-dependent model is developed to model the kinematics of surface growth for objects that can be generated by the curves on the surface, such as parasites and plants. This paper includes two main purposes for this model. The first one is to parametrize this model by using the quaternions and homothetic motions.Furthermore, we express the matrix representations of the surface-dependent growth model. The second one is to construct the surface-dependent growth model by using the growth velocity components related to the Darboux frame at each point of the generating curve. Moreover, to support the theory studied in the paper various illustrated examples are presented.

The existing literature discusses different strategies to solve a scalar ordinary differential equation using Lie point symmetries. We focus on three of these strategies in order to frame methods for finding solutions of non-linear systems of ordinary differential equations. These include Lie's integration theorem, method of successive reduction of order and the method of using the invariants of the admitted symmetry generators. Illustrative examples and those taken from mechanics are presented to highlight the use of these methods.