homogeneous Neumann boundary conditions

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On non-local reaction-diffusion system in a bounded domain

On non-local reaction-diffusion system in a bounded domain

domain. Since the integration is in , they impose the requirement that the diffusion takes place only in . The individuals may not enter nor leave . This is the analogous of what is called homogeneous Neumann boundary conditions in the literature. One analyzed the existence and uniqueness of solutions for (1.4) and found an exponential convergence to the mean value of the initial condition.

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Block pulse functions for solving fractional Poisson type equations with Dirichlet and Neumann boundary conditions

Block pulse functions for solving fractional Poisson type equations with Dirichlet and Neumann boundary conditions

with homogeneous boundary conditions u(x, ) = u(x, ) = u(, t) = u(, t) = . The ana- lytical solution of this problem is u(x, t) = xt(x – )(t – ). The graph of exact solution is shown in Figure . The graphs of numerical solutions for m = , ,  in some nodes (x, t) ∈ [, ] × [, ] are shown in Figures , , . From Examples  and Examples , it can be concluded that the numerical solutions approximate the exact solutions well as m grows.

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Boundary value problems for strongly nonlinear equations under a Wintner-Nagumo growth condition

Boundary value problems for strongly nonlinear equations under a Wintner-Nagumo growth condition

In this context, by using a different approach with respect to [4], we are able to prove existence results for solutions of (1) subjected to very general boundary value conditions including, as particular cases, Dirichlet, periodic, Sturm-Liouville and Neumann prob- lems. Our results extend those in [4] both for the presence of the function a inside the differential operators and for the great generality of the structure on the boundary con- ditions. Finally, we also provide some examples of application of our results, in which the operator is not homogeneous and grows exponentially at infinity.
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On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball

On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball

The paper is organized as follows. In the next section we study the properties of some integro-differential operators, which we then use throughout the paper. In Section  we investigate the Dirichlet problem for a polyharmonic equation, making use of the ex- plicit form of the Green function found in [–]. Then, in the following section, reducing Neumann problem (), () to the considered Dirichlet problem, we give the necessary and sufficient solvability condition for problem (), () with homogeneous boundary condi- tions. In the same way we consider in Section  the Neumann boundary value problem for the homogeneous equation with non-homogeneous boundary conditions. Finally, in Sec- tion  we study problem (), () in the general case. To present the necessary and sufficient conditions for solvability, here we apply the Almansi formula for constructing solutions to the Dirichlet problem.
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A solution decomposition for a singularly perturbed fourth-order problem

A solution decomposition for a singularly perturbed fourth-order problem

Our method of choice for finding a proper solution decomposition into an interior part (arising from solutions of third-order problems) and layer parts is the method of asymptotic expansions. This approach can, for instance, be found in [4, 10, 11, 13], where it is applied to second-order problems. Roughly rephrasing the rationale of asymptotic expansions, we consider a reduced problem, where formally ε is set to 0 and certain boundary conditions are neglected, to construct solution parts that are independent of ε. The misfit of certain boundary conditions is then corrected by boundary layer terms. As an ansatz for the boundary layer terms, we choose functions that exponentially decay away from the boundary.
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Global Existence and Blow-Up of Solutions for a Quasilinear Parabolic Equation with Absorption and Nonlinear Boundary Condition

Global Existence and Blow-Up of Solutions for a Quasilinear Parabolic Equation with Absorption and Nonlinear Boundary Condition

The global existence and blow-up for nonlinear parabolic equations have been extensively investigated by many authors in the last decades (see [1–6] and the references therein). In recent years, many authors have also studied bounds for the blow-up time in nonlinear parabolic problems by using differential inequality techniques (see [7–12]). In particular, Payne et al. [13] considered the following semilinear heat equation with nonlinear boundary condition

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Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

Abstract. This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic program- ming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton- Jacobi-Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in fi- nance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled sto- chastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.
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Asymptotic behavior of solutions to a class of coupled nonlinear parabolic systems

Asymptotic behavior of solutions to a class of coupled nonlinear parabolic systems

Levine, H., Zhang, Q.: The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values.. Li, H., Wang, X., Nie, Y., He, H.: Asympto[r]

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Exploring the Boundary Conditions of the Effect of Aesthetics on Perceived Usability

Exploring the Boundary Conditions of the Effect of Aesthetics on Perceived Usability

Evidence from studies prior to Tuch et al. suggested a directional relationship between aesthetics and usability in which increased aesthetics equaled increased usability. However, Tuch et al. showed that under certain circumstances the direction of the relationship was reversed—lower usability equaled lower perceived aesthetics. This finding was new, and it demonstrated the importance of exploring the contingencies and boundary conditions of the specific effects of manipulations of aesthetics and usability. Tuch et al. pointed out that additional research was necessary to understand the directions of these effects. They also pointed out that their results differed from prior studies in that users’ perceptions of the aesthetics of an interface changed after experience with the interface. However, their exploration of that particular contingency was limited to two observations, one made immediately before and the other immediately after users’ one-time interaction with the system. Recognizing this limitation, Tuch et al. encouraged future research that further manipulated aesthetics and usability to observe which effects occur under which conditions. Research Questions and Hypotheses
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An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions

An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions

Abstract In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equations. The re- sults of numerical experiments are presented to confirm the validity and applicability of the presented scheme.

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Solution of Thermo-Fluid problems in Bounded Domains via the Numerical Panel Method

Solution of Thermo-Fluid problems in Bounded Domains via the Numerical Panel Method

The classical panel method has been extensively used in external aero- dynamics to calculate ideal ow elds around moving vehicles or stationary structures in unbounded domains. However, the panel method, as a somewhat simpler implementation of the boundary element method, has rarely been employed to solve problems in closed complex domains. This paper aims at lling this gap and discusses the numerical solution of the Laplace equation in bounded domains via the numerical panel method. It is shown that the panel method is an ecient and accurate computational algorithm for the solution of this class of problems. Several test cases in heat conduction and internal ideal ow are presented to show that the numerical panel method can be used in closed domains regardless of the complexities in the geometry andor boundary conditions.
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On the prescribed variable exponent mean curvature impulsive system boundary value problems

On the prescribed variable exponent mean curvature impulsive system boundary value problems

This paper investigates the existence of solutions for prescribed variable exponent mean curvature impulsive system, with periodic-like, Dirichlet, and Neumann boundary value conditions, respectively. The proof of our main result is based upon the Leray-Schauder degree. The sufficient conditions for the existence of solutions are given.

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Conjugate Heat Transfer in a Developing Laminar Boundary Layer

Conjugate Heat Transfer in a Developing Laminar Boundary Layer

The above equations and boundary conditions were coded using the computer algebra system, Mathematica for both the quadratic and cubic temperature profiles. Two Reynolds numbers were considered, i.e., 1,000 and 500,000 as were three values of ′ , 1/2, 1/4 and 1/24. The results of the developed model were compared with those obtained using a computational fluid dynamics code.

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On the First Curve in the FučiK Spectrum with Weights for a Mixed
p Laplacian

On the First Curve in the FučiK Spectrum with Weights for a Mixed p Laplacian

over, the asymptotic behavior of these first curves was shown to depend on the supports of the weights. The case of the Neumann boundary conditions was considered later in [2] where, contrary to what happened in the Dirichlet case, the asymptotic behavior of the first curve did not depend on the supports of the weights.

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Approximate Solution of One dimensional Heat Conduction Problem

Approximate Solution of One dimensional Heat Conduction Problem

Abstract:In this paper, one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions is presented and a Homotopy Perturbation Method is utilized for solving the problem. Homotopy Perturbation Method provides continuous solution in contrast to finite difference method, which only provides discrete approximations. It is found that this method is a powerful mathematical tool and can be applied to a large class of linear and non linear problem in different fields of science, engineering and technology.
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On the Solvability of Nonlinear Boundary Value Problems on Time Scales

On the Solvability of Nonlinear Boundary Value Problems on Time Scales

Chapter 4 is devoted to the study of nonlinear scalar two-point boundary value problems where the corresponding linear homogeneous boundary value problem has a one dimensional solution space. Through use of the Lyapunov–Schmidt Procedure conditions are established to guarantee the existence of solutions to the these bound- ary value problems. We pay particular attention to second order equations subject to periodic boundary conditions. Results are obtained which significantly extend previ- ous work by Etheridge and Rodr´ıguez concerning the periodic behavior of nonlinear discrete dynamical systems [10].
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Global and blow up solutions for quasilinear parabolic equations with a gradient term and nonlinear boundary flux

Global and blow up solutions for quasilinear parabolic equations with a gradient term and nonlinear boundary flux

Equation (.) describes the diffusion of concentration of some Newtonian fluids through porous media or the density of some biological species in many physical phe- nomena and combustion theories (see [, ]). The nonlinear Neumann boundary value condition (.) can be physically interpreted as the nonlinear radial law (see, e.g., [, ]).

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Nonresonance between the first two Eigencurves of Laplacian for a Nonautonomous Neumann Problem

Nonresonance between the first two Eigencurves of Laplacian for a Nonautonomous Neumann Problem

They have proved the existence of nontrivial weak so- lutions for this problem for every given h ∈ L p (Ω) un- der some assumptions on the function g. In the case of Neumann elliptic problem J.-P. Gossez and P. Omari, have considered in [2] the following problem

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A Boundary Meshless Method for Neumann Problem

A Boundary Meshless Method for Neumann Problem

Another numerical technique for finding approxi- mate solutions of partial differential equation is the finite element method (FEM). The solution approach is based either on eliminating the differential equation completely or rendering the partial differential equation into an approximating system of ordering differential equation, which are then numerically integrated using standard techniques such as Euler's method, Runge- Kutta, etc. In solving partial differential equations, the primary challenge is to create an equation that approximates the equation under study, and is also numerically stable. This means that errors in the input and intermediate calculations do not accumulate and, therefore, do not cause the resulting output to be meaningless. In so doing, there are several ways, all of which have both advantages and disadvantages. The Finite Element Method is a good choice for solving partial differential equations over complicated domains (like cars and oil pipelines), when the domain changes (as during a solid state reaction with a moving boundary), when the desired precision varies over the entire domain, or when the solution lacks smoothness. For instance, in a frontal crash simulation it is possible to increase prediction accuracy in important areas like the front of the car and reduce it in its rear. The differences between FEM and FDM are:
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Block Unification Scheme for Elliptic,  Telegraph, and Sine Gordon Partial  Differential Equations

Block Unification Scheme for Elliptic, Telegraph, and Sine Gordon Partial Differential Equations

In this subsection, the performance of the EBNUM is tested on five problems, which include the Poisson equa- tion, Laplace equation subject to Neumann boundary conditions, Laplace equation subject to Dirichlet boundary conditions, Helmoltz equation, and the two-dimensional convection diffusion equation. In all the figures, the EBNUM is represented by uapprox and the exact solution is represented by uexact.

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