The purpose of this paper is to study the fluid-structure interaction (FSI) problem which is a simplified model to describe high frequency and small displacement oscillation of elastic structure in fluids. The elastic structure displacement is modeled by a fourth order nonlinear hyperbolic square equations, the motion of fluid is modeled by the time-dependent incompressible Navier-Stokes equations. we prove the existence of at least one weak solutions (global in time) to this problem by compactness method. The result both holds for two-dimensional and three-dimensional cases.

In the present paper initial problem for the integro-differential diffusion system with nonlocal nonlinear source is considered. The results on existence of local mild solution and nonexistence of global weak solution to the nonlinear integro-differential diffusion system are presented.

In the paper, we consider the local-in-time and the global-in-time infinity-ion-mass convergence of bipolar Euler-Maxwell systems by setting the mass of an electron me=1 and letting the mass of an ion mi→∞. We use the method of asymptotic expansions to handle the local-in-time convergence problem and find that the limiting process from bipolar models to unipolar models is actually decoupling, but not the vanishing of equations for the corresponding the other particle. Moreover, when the initial data is sufficiently close to the constant equilibrium state, we establish the global-in-time infinity-ion-mass convergence.

Using monotonicity methods, the Lagrange multiplier rule and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations are given in the final part of this paper.

The fifth order short pulse equation models the nonlinear propagation of optical pulses of a few oscillations duration in dielectric media. In particular, it models the propagation of circularly and elliptically polarized few-cycle solitons in a Kerr medium. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem associated with this equation.

in this work, we introduce an efficient meshless technique for solving the two-dimensional variable-order time-fractional mobile/immobile advection-diffusion model with Dirichlet boundary conditions. The main advantage of this scheme is to obtain a global approximation for this problem which reduces such problems to a system of algebraic equations. To approximate the first and fractional variable-order against the time, we use the finite difference relations. The proposed method is based on the Moving Kriging (MK) interpolation shape functions. To discretization this model in space variables, we use the MK interpolation. Duo to the fact that the shape functions of MK have Kronecker’s delta property, boundary conditions are imposed directly and easily. To illustrate the capability of the proposed technique on regular and irregular domains, several examples are presented in different kinds of domains and with uniform and nonuniform nodes. Also, we use this scheme to simulating anomalous contaminant diffusion in underground reservoirs.

This paper analyzes a SIS model for infectious diseases with two classes of individuals with different susceptibilities. It focuses in a transition function between both classes of susceptible individuals depending on the density of the infected population. A classification of all the possible bifurcation diagrams that the model can present is done. Specifically, some conditions for the simultaneous existence of backward bifurcation and multiple endemic states are shown.

In this paper we consider a class of chemotaxis models with two arbitrary constitutive functions g(u) and f(v). After having performed a complete symmetry group classification with respect to them the reduced systems are derived. By considering g(u) of the logistic form wide classes of exact solutions are found.

In the paper, we devote to broadening the current global regularity results for the two-dimensional magnetic B\’{e}nard fluid equations. We study three cases: (i) fractional Laplacian dissipation $(-\Delta)^\alpha{u}$, partial magnetic diffusion $(\partial_{x_2x_2}b_1,\partial_{x_1x_1}b_2)$ and Laplacian thermal diffusivity $\Delta\theta$; (ii) partial fractional dissipation $(\Lambda^{2\alpha}_{x_2}u_1,\Lambda^{2\alpha}_{x_1}u_2)$, partial magnetic diffusion $(\partial_{x_2x_2}b_1,\partial_{x_1x_1}b_2)$ and Laplacian thermal diffusivity $\Delta\theta$; (iii) partial fractional magnetic diffusion $(\Lambda^{2\beta}_{x_2}b_1,\Lambda^{2\beta}_{x_1}b_2)$, Laplacian thermal diffusivity $\Delta\theta$ and without Laplacian dissipation $\Delta{u}$ (i.e., $\mu=0$)), and establish the global regularity for each cases.

A system of boundary-domain integral equations (BDIEs) is obtained from the Dirichlet problem for the diffusion equation in non-homogeneous media defined on an exterior two-dimensional domain. We use a parametrix different from the one employed by in . The system of BDIEs is formulated in terms of parametrix-based surface and volume potentials whose mapping properties are analysed in weighted Sobolev spaces. The system of BDIEs is shown to be equivalent to the original boundary value problem and uniquely solvable in appropriate weighted Sobolev spaces suitable for unbounded domains.

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.

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.

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.

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.

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.

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.

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.

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.