Numerical solution of integrodifferential equations with convolution integrals

Archive of Applied Mechanics - A numerical solution is presented for the solution of integrodifferential equations involving convolution integrals. These equations can be viewed as a generalization...     

On a class of scattering equations

In this paper a class of conservative wave equations treated by Broer and Peletier is considered when a single localised scatterer is present. A criterion for stability in the energy norm is derived. The formal solution of the scattering problem is given. The relation between the location of poles of the scattering matrix, the occurrence of standing wave solutions and the energy criterion is discussed.     

Oscillation of a class of nonlinear partial difference equations with continuous variables

We consider a class of nonlinear partial difference equations with continuous variables. Some oscillation criteria are obtained using an integral transformation and inequalities.     

Nonlinear dynamics of flexible slender structures moving in a limited space with application in nuclear reactors

Nonlinear Dynamics - This paper deals with the modelling and dynamic analysis of thin or slender flexible bodies characterized by axial motion, contacts and friction interaction. Such mechanical...     

On a class of constitutive equations for viscoelastic liquids

Simple rheological equations that describe non-linear viscoelastic phenomena in polymeric liquids have long attracted the attention of many rheologists. Although there are many ways of deriving such equations, only one concept is considered here. This concept is based on the introduction of an internal parameter, the recoverable strain tenson, and arises from a special kinematic study together with the formalism of irreversible thermodynamics. The main part of the paper sets out the theory for a single mode but a multimode extension is demonstrated towards the end and is compared with experimental data. Finally some of the problems that remain unsolved in the theory are discussed.The aim of this paper is to acquaint rheologists with the author's views as the model rheological equations he developed have recently been discussed in the literature without his participation.     

Numerical study of a nonlinear integrodifferential equation

I.IntroductionItiswell-knobal.nthatKorteweg-deVriesequationisacanonicalmodeltodescribethebalanceofthenonlineareffectandthedispersiveeffectofaphysicalsystem.Thisequationpossessestheso-called'soliton"solution,whichhasbeenfoundnumericallybyZabuskyandKruskall'].Ho-c'Jlever,sometimesthebalanceofnonlinearityanddispersionofasystemmayleadtoa,integroditTerentialequationinsteadofadifferentialequation.Forinstance,inthestudyofvortexbreakdownofanunboundedrotatingfluidLeibovich12]derivedfollowingnonline…     

On a class of quasilinear Schrodinger equations

A type of quasilinear Schrodinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sutficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained.     

Adaptive fault compensation control for a class of nonlinear systems with unknown time-varying delayed faults

An adaptive approximation design for the fault compensation (FC) control is addressed for a class of nonlinear systems with unknown multiple time-delayed nonlinear faults. The magnitude and occurrence time of the multiple faults with unknown time-varying delays are unknown. The function approximation technique using neural networks is employed to adaptively approximate the unknown nonlinear effects and changes in model dynamics due to the time-delayed faults. We design an adaptive memoryless FC control system with a prescribed performance bound to compensate the faults and to guarantee the transient performance of the tracking error from unexpected changes of system dynamics. The adaptive laws for neural networks and the bound of residual approximation errors are derived using the Lyapunov stability theorem, which are used for proving that the tracking error is preserved within the prescribed performance bound regardless of unknown multiple time-delayed nonlinear faults. Simulation examples are presented for illustrating the effectiveness of the proposed control methodology     

The hölder continuity of generalized solutions of a class quasilinear parabolic equations

Let A cud B satisfy the Structural conditions (2), the local Hölder continuityinterior to Q=G×(0, T) is proved for the generalized solutions of quasilinearparabolic equations as follows: u₂ - divA(x, t,u,∇u) + B(x, t, u, ∇u)=0     

Positive solution of a class of equations involving noncompact mappings

In this paper, we define a generalized relative degree for A-proper mappings from a relative open subset of a Banach space into another Banach space and introduce the concepts of generalized P-compact and P₁-compact mappings. Next, we show several existence theorems of positive solutions for the equations involving these mappings. Our theorems improve and extend some recent results.     

Analytic solutions of a class of nonlinear partial differential equations

An approach is presented for computing the adjoint operator vector of a class of nonlinear （that is, partial-nonlinear） operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear （partial-nonlinear and including all linear） and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.     

GLOBAL ATTRACTIVITY FOR A CLASS OF NONLINEARDELAY DIFFERENCE EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｇｌｏｂａｌａｔｔｒａｃｔｉｖｉｔｙｏｆｔｈｅｎｏｎｌｉｎｅａｒｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｘｎ+ａｎｘｎ+ｆ(ｎ ,∑0ｓ=-ｋ ｑｓ,ｎｘｓ+ｎ) =0　 (ｎ=0 ,1 ,2 ,… ) . ( 1 )ＴｈｅｉｎｉｔｉａｌｖａｌｕｅｏｆＥｑ .( 1 )ｉｓｘｓ =φｓ　 (ｓ=-ｋ ,-ｋ+ 1 ,… ,-1 ,0 ) . ( 2 )Ｉｎｔｈｅｓｅｑｕｅｌ,ｗｅａｌｗａｙｓｓｕｐｐｏｓｅｔｈａｔＤ1) ａｎ ｉｓａｎｏｎｎｅｇａｔｉｖｅｒｅａｌｓｅｑｕｅｎｃｅ ,0 ≤ａｎ <1ａｎｄｋｉｓａｐｏｓｉｔｉｖｅ…     

Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates

This paper introduces an efficient numerical algorithm for solving a significant class of linear and nonlinear time-fractional partial differential equation governed by Fredholm–Volterra operator in the sense of Robin conditions. A direct approach based on the normalized orthonormal function systems that fitted from the Gram–Schmidt orthogonalization process is utilized to transcribe the problem under study into appropriate Hilbert space. Some functional analysis theories such as upper error bound and convergence behavior under some assumptions which give the hypothetical premise of the proposed calculation are likewise talked about. Mathematical properties of the numerical results obtained are analyzed as well as general features of many numerical solutions have been identified. At long last, the used outcomes demonstrate that the present calculation and mimicked toughening give a decent planning procedure to such models.     

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺｈａｏＪｉｅ－ｍｉｎ（赵杰民）;ＨｕａｎｇＫｅ－ｌｅｉ（黄克累）...     

On the boundary value problems for a class of ordinary differential equations with turning points

In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales. The paradox in [1] and the variational approach in [2] are avoided. The uniformly valid asymptotic approximations of solutions have been constructed. We also study the case which does not exhibit resonance.