Homogeneous Boundary Research Articles

A Finite-Difference Approximation for the One- and Two-Dimensional Tempered Fractional Laplacian

This paper provides a finite-difference discretization for the one- and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions. The main ideas are to, respectively, use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian. Then, we give the truncation errors and prove the convergence. Numerical experiments verify the convergence rates of the order $$O(h^{2-2s})$$.

Global existence, boundedness and asymptotic behavior to a chemotaxis model with singular sensitivity and logistic source

ABSTRACT This article deals with the chemotaxis model with singular sensitivity and logistic source under homogenous Neumann boundary condition in a smooth bounded domain , with and for all s>0 with . For , we show that the system admits a global classical solution that provides , and . Furthermore, for N=2, under the assumptions above, we obtain the boundedness and asymptotic behavior of solutions that provide , , and μ sufficiently large.

Extinction and Decay Estimates of Solutions for a Non-Newton Polytropic Filtration System

This paper mainly deals with extinction and non-extinction of weak solutions for a non-Newton polytropic filtration system coupled with non-local source terms under homogeneous Dirichlet boundary condition by comparing the exponents of nonlinear terms. Particularly, precise decay estimates of extinction solutions in the whole dimensional space are also established.

Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System

In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology.

A new existence result for the boundary value problem of p-Laplacian equations with sign-changing weights

In this paper, a new existence result for the homogeneous Dirichlet boundary value problem of p-Laplacian equations with sign-changing weights which may not be in $$L^{1}$$ is presented. Our approach is based on the nonlinear alternative of Leray–Schauder type theorem.

A Method of Accelerating the Convergence of Computational Fluid Dynamics for Micro-Siting Wind Mapping

To assess wind resources, a number of simulations should be performed by wind direction, wind speed, and atmospheric stability bins to conduct micro-siting using computational fluid dynamics (CFD). This study proposes a method of accelerating CFD convergence by generating initial conditions that are closer to the converged solution. In addition, the study proposes the ‘mirrored initial condition’ (IC) using the symmetry of wind direction and geography, the ‘composed IC’ using the vector composition principle, and the ‘shifted IC’ which assumes that the wind speed vectors are similar in conditions characterized by minute differences in wind direction as the well-posed initial conditions. They provided a significantly closer approximation to the converged flow field than did the conventional initial condition, which simply assumed a homogenous atmospheric boundary layer over the entire simulation domain. The results of this study show that the computation time taken for micro-siting can be shortened by around 35% when conducting CFD with 16 wind direction sectors by mixing the conventional and the proposed ICs properly.

On a certain property of a regular difference operator with variable coefficients

We consider a regular difference operator with variable coefficients in a bounded domain. It will be proved that this operator maps continuously and bijectively the Sobolev space of order k with the homogeneous Dirichlet boundary conditions to the subspace of Sobolev space of order k with nonlocal boundary conditions on the shifts of the boundary. This allows to apply the results obtained for nonlocal elliptic problems to the investigation of elliptic differential-difference equations.

Исследование состояний равновесия второго рода уравнения Курамото-Сивашинского с однородными условиями Неймана

Исследование состояний равновесия второго рода уравнения Курамото-Сивашинского с однородными условиями Неймана

Neural network-based adaptive selection CFAR for radar target detection in various environments

Constant false alarm rate (CFAR), a target detection method commonly used in the radar systems, has an inconsistent performance against various environments. For improving the radar detectability, this paper proposes a novel scheme of radar target detection using neural network-based adaptive selection CFAR. The proposed method employs cell-averaging, ordered-statistic, greatest-of and smallest-of CFAR thresholds as the basis of references. The pattern of those threshold values combined with the cell under test signal value will be identified and classified by the neural network to compute the raw threshold. Then, the final threshold is selected depending on the nearest value between raw and four referenced CFARs. The performance of the proposed method is examined against three possible cases of the radar systems including homogeneous background, multiple targets and clutter boundary. The result of this research shows that the proposed method outperforms the classical CFARs due to the adaptive selection algorithm can select properly among referenced CFARs against the given cases particularly in the homogeneous and multiple target environments.

Bifurcation structure of nonconstant positive steady states for a diffusive predator-prey model.

In this paper, we make a detailed descriptions for the local and global bifurcation structure of nonconstant positive steady states of a modified Holling-Tanner predator-prey system under homogeneous Neumann boundary condition. We first give the stability of constant steady state solution to the model, and show that the system exhibits Turing instability. Second, we establish the local structure of the steady states bifurcating from double eigenvalues by the techniques of space decomposition and implicit function theorem. It is shown that under certain conditions, the local bifurcation can be extended to the global bifurcation.

MODELLING PARAMETERS AND IMPACTS OF FOUR EXTRATROPICAL CYCLONES UNDER FUTURE CLIMATE SCENARIOS

Coastal zone is among the most vulnerable areas of the Earth to global warming, firstly, due to anticipated mean sea level rise, and secondly, regarding changes in storm activity. In Europe, much of the high-impact weather events are associated with extratropical cyclones (ETC). It is highly possible that tropical cyclones will get stronger under future climate conditions, however projections for ETC-s are still far more mixed. The study at hand is an improved extension to that of Mäll et al. (2017) where the authors aimed to study how an individual extreme storm (2005 Gudrun) would change under future climate conditions. The main aim is to learn whether the similar results are found for four different (tracks, thermal conditions) ETC-s under improved methodology and homogenous initial and boundary conditions in order to decrease uncertainty and draw stronger climatological generalizations. The study area is the Baltic Sea region and more specifically Estonia.

Stress-heat flux characterization of linear dynamic coupled thermoelasticity for an inhomogeneous isotropic infinite cylinder under plane strain conditions and zero heat flux normal to the plane

Stress-heat flux characterization of linear dynamic coupled thermoelasticity for an inhomogeneous isotropic infinite cylinder under plane strain conditions and zero heat-flux normal to the plane is presented. It is shown that for a bounded cross-section of the cylinder, a 3D stress-heat flux process is generated by a 2D one, and a uniqueness theorem for the associated 2D initial-boundary value problem is established. In addition, an asymptotic approach to the 2D stress-heat flux initial-boundary value problem, in the form of a power series with respect to a small thermoelastic coupling field, is proposed. Also, Green' s formulas for time-periodic complex-valued solutions to 2D stress-heat flux field equations are obtained; and the existence of a globally constrained real-valued periodic and attenuated on the time-axis stress-heat flux mode satisfying homogeneous natural boundary conditions is proved. The stress-heat flux characterization covers a large class of FGM's with physical properties smoothly distributed over the cross-section of the infinite cylinder. The results obtained are complementary to those of linear dynamic coupled thermoelasticity published up to date and should prove useful for a number of researchers in the field.

The Kuramoto–Sivashinsky Equation. A Local Attractor Filled with Unstable Periodic Solutions

A periodic boundary value problem is considered for one of the first versions of the Kuramoto–Sivashinsky equation, which is widely known in mathematical physics. Local bifurcations in a neighborhood of spatially homogeneous equilibrium points are studied in the case when they change stability. It is shown that the loss of stability of homogeneous equilibrium points leads to the occurrence of a two-dimensional local attractor on which all solutions are periodic functions of time, except for one spatially inhomogeneous state. The spectrum of frequencies of this family of periodic solutions fills the entire number line, and all of them are unstable in the sense of Lyapunov’s definition in the metric of the phase space (the space of initial conditions) of the corresponding initial boundary value problem. As the phase space, a Sobolev functional space natural for this boundary value problem is chosen. Asymptotic formulas are given for periodic solutions filling the two-dimensional attractor. To analyze the bifurcation problem, analysis methods for an infinite-dimensional dynamical system are used: the integral (invariant) manifold method combined with the methods of the Poincare normal form theory and asymptotic methods. Analyzing the bifurcations for the periodic boundary value problem is reduced to analyzing the structure of the neighborhood of the zero solution to the homogeneous Dirichlet boundary value problem for the equation under consideration.

On the existence and long-time behavior of solutions to stochastic three-dimensional Navier–Stokes–Voigt equations

ABSTRACTWe consider the 3D stochastic Navier–Stokes–Voigt equations in bounded domains with the homogeneous Dirichlet boundary condition and infinite-dimensional Wiener process. First, we prove the existence and uniqueness of solutions to the problem. Then we investigate the mean square exponential stability and the almost sure exponential stability of the stationary solutions.

Bifurcation analysis of coexistent state in a delayed two-species predator-prey model

ABSTRACTIn this paper, we consider a delayed two-species predator-prey model with general functional response under the homogeneous Neumann boundary condition. We discuss the stability of the trivial and semi-trivial solutions and obtain the spatially nonhomogeneous bifurcation solutions stemming from the semi-trivial trivial solutions and . Besides, the stability and some results of Hopf bifurcation at the spatially nonhomogeneous bifurcation steady-state solutions are investigated by analyzing the distribution of the eigenvalues. The method we applied here is mainly based on spectral analysis, comparison principle, Lyapunov-Schmidt reduction, and bifurcation theory.

Complete quenching phenomenon for a parabolic p-Laplacian equation with a weighted absorption

Throughout this paper, we mainly consider the parabolic p-Laplacian equation with a weighted absorption u_{t}-operatorname{div} (|nabla u|^{p-2}nabla u )=-lambda |x|^{alpha} {chi}_{{u>0}}u^{-beta} in a bounded domain Omegasubseteqmathbb{R}^{n} (ngeq1) with Lipschitz continuous boundary subject to homogeneous Dirichlet boundary condition. Here lambda>0 and alpha>-n are parameters, and betain(0,1) is a given constant. Under the assumptions u_{0}in W_{0}^{1,p}(Omega)cap L^{infty}(Omega), u_{0}geq0 a.e. in Ω, we can establish conditions of local and global in time existence of nonnegative solutions, and show that every global solution completely quenches in finite time a.e. in Ω. Moreover, we give some numerical experiments to illustrate the theoretical results.

Error Analysis of Chebyshev Spectral Element Methods for the Acoustic Wave Equation in Heterogeneous Media

This work concerns the error analysis of the spectral element method with Gauss–Lobatto–Chebyshev collocation points with the implicit Newmark average acceleration scheme for the two-dimensional acoustic wave equation. The analysis is restricted to homogeneous Dirichlet boundary conditions, constant compressibility and variable density. The proposed error estimates are optimal with respect to the mesh parameter although suboptimal on the polynomial degree. Numerical examples illustrate the theoretical results.

Solvability homogeneous Riemann-Hilbert boundary value problem with several points of turbulence

Solvability homogeneous Riemann-Hilbert boundary value problem with several points of turbulence

Existence and uniqueness of entropy solutions to nonlinear parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent

In this paper, we prove the existence and uniqueness of entropy solution to nonlinear parabolic problem with homogeneous Dirichlet boundary conditions with $$L^1$$ -data. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. The general assumptions and the nonlinear semigroup theory are considered to prove the existence and uniqueness of mild solution satisfying the $$L^1$$ -comparison principle. Moreover, under the same general assumptions and some a-priori estimations of the sequence of mild solutions, we obtain the existence and uniqueness of weak solution. Finally, we prove the existence and uniquess of the renormalized solution which is equivalent to the existence and uniqueness of entropy solution.

Delay-induced Hopf bifurcation in a diffusive Holling\u2013Tanner predator\u2013prey model with ratio-dependent response and Smith growth

In this paper, we study a diffusion Holling–Tanner predator–prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration technique and eigenvalue analysis to get the local stability and a Hopf bifurcation at the positive equilibrium. Secondly, by choosing the constant related to delay as bifurcation parameter we obtain periodic solutions near the positive equilibrium. Besides, by using center manifold theory and normal form theory we reflect the stability with Hopf bifurcating periodic solution and bifurcating direction.