The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

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.

A NOTE ON PROBABILISTIC INTERPRETATION FOR QUASILINEAR MIXED BOUNDARY PROBLEMS

Solutions of quasilinear mixed boundary problems for the some parabolic an elliptic partial differential equations are interpreted as solutions of a kind of backward stochastic differential equations, which are associated with the classical Ito forward stochastic differential equations with reflecting 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.

Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev

.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.

TWO-SCALE FEM FOR ELLIPTIC MIXED BOUNDARY VALUE PROBLEMS WITH SMALL PERIODIC COEFFICIENTS

Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual approximate error estimates; Main results.

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.

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.

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

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI-PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The results show that the stress intensity factor is identical with the mode Ⅲ stress intensity factor independent of the conducting length.But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.

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.

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.

THREE SOLUTIONS FOR A CLASS OF GRADIENT MIXED BOUNDARY VALUE SYSTEMS DEPENDING ON TWO PARAMETERS

In this paper we discuss the existence of at least three solutions for a class of gradient mixed boundary value systems. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal., 70：9（2009）,3084-3089].

Superlinear Elliptic Equation with Mixed Boundary Value in Annular Domain

In this paper,we study superlinear elliptic equations with mixed boundary value conditions in annular domains.It is assumed that the nonlinearities depend on the derivative terms.Some results about existence of solutions are established by using the Nehari manifold technique,as well as iterative 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.