Recently in several papers the boundary element method has been applied to non-linear problems. In this paper we extend the analysis to strongly nonlinear boundary value problems. We shall prove the convergence and the stability of the Galerkin method in Lp spaces. Optimal order error estimates in Lp space then follow. We use the theory of A-proper mappings and monotone operators to prove convergence of the method. We note that the analysis includes the u4 -nonlinearity, which is encountered in heat radiation problems.

In the framework of Mond-Weir duality a new equivalence between nonlinear programming and a matrix game is given. Finally, certain conclusions about convex programming with nested maxima and matrix games are also included.

In this paper, the generalised complementarity problem studied by Parida and Sen [13] is further extended. The extended problem appears to be more general and unifying. Characterisations of solutions to this extended problem are given. Some existence results derived by these characterisations are presented. An application of the extended problem to the quasi-variational inequalities of obstacle type is considered.

Nonlinear convective roll cells that develop in thin layers of magnetized ferrofluids heated from above are examined in the limit as the wavenumber of the cells becomes large. Weakly nonlinear solutions of the governing equations are extended to solutions that are valid at larger distances above the curves of marginal stability. In this region, a vortex flow develops where the fundamental vortex terms and the correction to the mean are determined simultaneously rather than sequentially. The solution is further extended into the nonlinear region of parameter space where the flow has a core-boundary layer structure characterized by a simple solution in the core and a boundary layer containing all the harmonics of the vortex motion. Numerical solutions of the boundary layer equations are presented and it is shown that the heat transfer across the layer is significantly greater than in the conduction state.

Consider the neutral delay differential equation

where p ∈ R, τ ≥ 0, q1 > 0, σ1 ≥ 0, for i = 1, 2, …, k. We prove the following result.

Theorem. A necessary and sufficient condition for the oscillation of all solutions of Eq. (1) is that the characteristic equation

has no real roots.

A detailed analytical and numerical study is made of the deformation of highly elastic circular cylinders and tubes produced by steady rotation about the axis of symmetry. Explicit results are obtained through the use of Ogden's strain–energy function for incompressible isotropic elastic materials which, as well as being analytically convenient, is capable of reproducing accurately the observed isothermal behaviour of vulcanized rubber over a wide range of deformations. The three problems of steady rotation considered here concern (i) a tube shrink-fitted to a rigid spindle, (ii)an unconstrained tube, and (iii) a solid cylinder. In each case a set of restictions on the material constans appearing in the strain–energy function is stated which ensures that a tubular of cylindrical shape-preserving deformation exists for all angular spees and that, for problems (i) and (iii), there is no other solution. In connection with problems (ii) and (iii) values of the material constans are also given which correspond to the bifuraction or non-existence of soultions. Enegry consideration are used to determine the local stability of the various solutions obtained.

Conservation laws for partial differential equations can be characterised by an operator, the characteristic and a condition involving the adjoint of the Fréchet derivatives of this operator and the operator defining the partial differential equation. This approach was developed by Anco and Bluman and we exploit it to derive conditions for second-order parabolic partial differential equations to admit conservation laws. We show that such partial differential equations admit conservation laws only if the time derivative appears in one of two ways. The adjoint condition, however, is a biconditional, and we use this to prove necessary and sufficient conditions for a certain class of partial differential equations to admit a conservation law.

We show how a short and elementary proof can be provided for a recently-published inequality ([6], [4]) which has found a number of applications.

In this paper we study the effect of forced and free convection heat transfer on flow in an axisymmctric tube whose radius varies slowly in the axial direction. Asymptotic series expansions in terms of a small parameter ∈, which is a measure of the radius variation, are obtained for the velocity components, pressure and temperature on the assumption that the Reynolds number (R) is of order one. The effect of the free convection parameter or Grashof number (G) on the axial velocity, temperature distribution, shear stress and heat flux at the wall are discussed quantitatively for a locally constricted tube.

This paper presents a method for the inverse fractional matching problem. We show that the dual of this inverse problem can be transformed into the circulation flow problem on a directed bipartite graph which can be solved easily. We also give an algorithm to obtain the primal optimum solution of the inverse problem from its dual optimum solution by solving a shortest path problem. Furthermore, we generalize this method to solve the inverse symmetric transportation problem.

Recursive parametric series solutions are developed for polynomial ODE systems, based on expanding the system components in series of a form studied by Weiss. Individual terms involve first-order driven linear ODE systems with variable coefficients. We consider Lotka-Volterra systems as an example.

The existence of an inertial manifold for a reaction-diffusion equation model of the chemostat is established.

This paper deals with robust guaranteed cost control for a class of linear uncertain descriptor systems with state delays and jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. Based on stability theory for stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost controllers is derived. In terms of the LMI (linear matrix inequality) approach, a linear state feedback controller is designed to stochastically stabilise the given system with a cost function constraint. A convex optimisation problem with LMI constraints is formulated to design the suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.

In Convex Structures and Economic Theory, Nikaideo analysed, inter alia, a circulating capital Leontief model where final demand could exhibit either proportional or non-proporaitonal growth. This paper extends his analsis to a fixed capital modee. Analogues of Nikaido's results are derived for the closed model and for the open model under blaanced grwoth. However, the results obtained here for the open model with unbalanced growth are weaker than Nikaido's.

We treat a single-server vacation queue with queue-length dependent vacation schedules. This subsumes the single-server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch-Markovian arrival process (BMAP). We derive the queue-length distribution at departure epochs. By using a semi-Markov process technique, we obtain the Laplace-Stieltjes transform of the transient queue-length distribution at an arbitrary time point and its limiting distribution

We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the organising centre is a pitchfork singularity for both the adiabatic and diabatic reactors. However, unlike the adiabatic reactor, Hopf bifurcations may occur in the diabatic reactor. We construct the degenerate Hopf bifurcation curve by determining the double-Hopf locus. When the steady-state and degenerate Hopf bifurcation diagrams are combined it is found that there are 23 generic steady-state diagrams over the parameter region of interest. The implications of these structures from the perspective of flammability in the CSTR are discussed.

The error analysis of an algorithm for generating an approximation of degree n − 1 to an nth degree Bézier curve is presented. The algorithm is based on observations of the geometric properties of Bézier curves which allow the development of detailed error analysis. By combining subdivision with a degree reduction algorithm, a piecewise approximation can be generated, which is within some preset error tolerance of the original curve. The number of subdivisions required can be determined a priori and a piecewise approximation of degree m can be generated by iterating the scheme.