EXISTENCE OF MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.

Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions

The unusual properties of quasicrystals(QCs)have attracted tremendous attention from researchers.In this paper,a semi-analytical solution is presented for the static response of a functionally graded(FG)multilayered two-dimensional(2 D)decagonal QC rectangular plate with mixed boundary conditions.Based on the elastic theory of FG 2 D QCs,the state-space method is used to derive the state equations composed of partial differential along the thickness direction.Besides,the Fourier series expansion and the differential quadrature technique are utilized to simulate the simply supported boundary conditions and the mixed boundary conditions,respectively.Then,the propagator matrix which connects the field variables at the upper interface to those at the lower interface of any homogeneous layer can be derived based on the state equations.Combined with the interface continuity condition,the static response can be obtained by imposing the sinusoidal load on the top surfaces of laminates.Finally,the numerical examples are presented to verify the effectiveness of this method,and the results are very useful for the design and understanding of the characterization of FG QC materials in their applications to multilayered systems.

DOUBLE FLIP MOVE FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS

This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip.Both symmetric and approximately symmetric models are considered.We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.

On the Rotating Navier-Stokes Equations with Mixed Boundary Conditions

The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided.

The Asymptotics of the Heat Semigroup for a General Bounded Domain with Mixed Boundary Conditions

Small-time asymptotics of the trace of the heat semigroup θ（t）=Σv=1x exp（-tμv）. where {μv} are the eigenvalues of the uegative Laplacian -Δ= -Σβ=12（/xβ）2 in the （x1, x2）-plane. is studied for a general bounded domain Ω with a smooth boundary Ω. where a finite number of Dirichlet. Neumann and Robin boundary conditions, on the piecewise smooth parts Γi（i=1, ..., n） of )Ω such that)Ω=∪i=1nΓ are considered. Some geometrical properties associated with Ω are determined

AN ITERATIVE PROCEDURE FOR DOMAIN DECOMPOSITION METHOD OF SECOND ORDER ELLIPTIC PROBLEM WITH MIXED BOUNDARY CONDITIONS

This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.

Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation

The solution of boundary value problems(BVP)for fourth order differential equations by their reduction to BVP for second order equations,with the aim to use the available efficient algorithms for the latter ones,attracts attention from many researchers.In this paper,using the technique developed by the authors in recent works we construct iterative method for a problem with complicated mixed boundary conditions for biharmonic equation which is originated from nanofluidic physics.The convergence rate of the method is proved and some numerical experiments are performed for testing its dependence on a parameter appearing in boundary conditions and on the position of the point where a transmission of boundary conditions occurs.

Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by hp-FEM

We present a proof of the discrete maximum principle(DMP)for the 1D Poisson equation−u"=f equipped with mixed Dirichlet-Neumann boundary conditions.The problem is discretized using finite elements of arbitrary lengths and polynomial degrees(hp-FEM).We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.

A Global Carleman Inequality and Exact Controllability of Parabolic Equations with Mixed Boundary Conditions

This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary.

GENERALIZED STROH FORMALISM FOR ANISOTROPIC ELASTICITY FOR GENERAL BOUNDARY CONDITIONS

The Stroh formalism is most elegant when the boundary conditions are simple, namely,they are prescribed in terms of traction or displacement.For mixed boundary conditions such as there for a slippery boundary,the concise matrix expressions of the Stroh formalism are destroyed.We present a generalized Stroh formalism which is applicable to a class of general boundary conditions.The general boundary conditions in- clude the simple and slippery boundary conditions as special cases.For Green's functions for the half space, the general solution is applicable to the case when the surface of the half-space is a fixed,a free,a slippery, or other more general boundary.For the Griffith crack in the infinite space,the crack can be a slit-like crack with free surfaces,a rigid line inclusion(which is sometimes called an anticrack),or a rigid line with slippery surface or with other general surface conditions.It is worth mention that the modifications required on the Stroh formalism are minor.The generalized formalism and the final solutions look very similar to those of unmodified version.Yet the results are applicable to a rather wide range of boundary conditions.

Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions

In this paper, a brand-new wavelet-homotopy Galerkin technique is developed to solve nonlinear ordinary or partial differential equations. Before this investigation,few studies have been done for handling nonlinear problems with non-uniform boundary conditions by means of the wavelet Galerkin technique, especially in the field of fluid mechanics and heat transfer. The lid-driven cavity flow and heat transfer are illustrated as a typical example to verify the validity and correctness of this proposed technique. The cavity is subject to the upper and lower walls’ motions in the same or opposite directions.The inclined angle of the square cavity is from 0 to π/2. Four different modes including uniform, linear, exponential, and sinusoidal heating are considered on the top and bottom walls, respectively, while the left and right walls are thermally isolated and stationary.A parametric analysis of heating distribution between upper and lower walls including the amplitude ratio from 0 to 1 and the phase deviation from 0 to 2π is conducted. The governing equations are non-dimensionalized in terms of the stream function-vorticity formulation and the temperature distribution function and then solved analytically subject to various boundary conditions. Comparisons with previous publications are given,showing high efficiency and great feasibility of the proposed technique.

A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN

Let M be an n-dimensional compact Riemannian manifold with or without boundary,and its Ricci curvature Ric M≥n-1.The paper obtains an inequality for the first eigenvalue η 1 of M with mixed boundary condition,which is a generalization of the results of Lichnerowicz,Reilly,Escobar and Xia.It is also proved that η 1≥n for certain n-dimensional compact Riemannian manifolds with boundary,which is an extension of the work of Cheng,Li and Yau.

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

Dynamic response analysis of a multiple-beam structure subjected to a moving load

In this study,the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated.The boundary conditions and properties of each beam vary,and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations.By examining a high-speed railway(HSR)with mixed boundary conditions,the rationality for the newly proposed method is verified,the difference in simulated multiple-beam models with different beam numbers is explored,and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined.Results suggest that the number of beams in the model should be as close to the actual beam number as possible.Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure.Neglecting the track-structure can overestimate the resonant speed of a high-speed railway,simply-supported beam bridge.The effective interval of foundation stiffness(EIFS)can provide a reference for future engineering designs.

A ROBUST AND ACCURATE SOLVER OF LAPLACE＇S EQUATION WITH GENERAL BOUNDARY CONDITIONS ON GENERAL DOMAINS IN THE PLANE

A robust and general solver for Laplace＇s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, its performance is demonstrated via some challenging numerical tests.

Existence theory for Rosseland equation and its homogenized equation

The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition

Based on consolidation equations proposed for unsaturated soil, an analytical solution for 1D consolidation of an unsaturated single-layer soil with nonhomogeneous mixed boundary condition is developed. The mixed boundary condition can be used for special applications, such as tests occur in laboratory. The analytical solution is obtained by assuming all material parameters remain constant during consolidation. In the derivation of the analytical solution, the nonhomogeneous boundary condition is first transformed into a homogeneous boundary condition. Then, the eigenfunction and eigenvalue are derived according to the consolidation equations and the new boundary condition. Finally, using the method of undetermined coefficients and the orthogonal relation of the eigenfunction, the analytical solution for the new boundary condition is obtained. The present method is applicable to various types of boundary conditions. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with mixed boundary condition.

Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs

In this paper,we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs.Firstly,we prove the local existence of solutions via Schauder fixed point theorem.Then,under certain conditions we obtain the estimates of quenching time and quenching rate.Finally,numerical experiments are shown to explain the theoretical results.

Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect

Due to its highly oscillating solution,the Helmholtz equation is numerically challenging to solve.To obtain a reasonable solution,a mesh size that is much smaller than the reciprocal of the wavenumber is typically required(known as the pollution effect).High-order schemes are desirable,because they are better in mitigating the pollution effect.In this paper,we present a high-order compact finite difference method for 2D Helmholtz equations with singular sources,which can also handle any possible combinations of boundary conditions(Dirichlet,Neumann,and impedance)on a rectangular domain.Our method is sixth-order consistent for a constant wavenumber,and fifth-order consistent for a piecewise constant wavenumber.To reduce the pollution effect,we propose a new pollution minimization strategy that is based on the average truncation error of plane waves.Our numerical experiments demonstrate the superiority of our proposed finite difference scheme with reduced pollution effect to several state-of-the-art finite difference schemes,particularly in the critical pre-asymptotic region where kh is near 1 with k being the wavenumber and h the mesh size.