SIAM Journal on Applied Mathematics

A multiple-scale perturbation method which was previously used to obtain solutions of some weakly nonlinear elliptic Dirichlet boundary-value problems on a semi-infinite strip is here extended to apply to problems on the upper half-plane. This is ...

This paper is concerned with the static, one-dimensional modelling of a semiconductor device (namely the $pn$-junction) when a bias is applied. The governing equations are the well-known equations describing carrier transport in a semiconductor which ...

There are several nonlinear bifurcation problems which involve multiple bifurcation parameters (“specified inputs”). Often there is a corresponding “perturbed” problem associated with the bifurcation problem which models imperfections. Instead of ...

Three-dimensional motions of a cantilever tube carrying an incompressible fluid and having rotational symmetry about the vertical axis are examined for bifurcating oscillatory solutions. The system behavior depends on two parameters, $\rho $, the flow ...

The modulations of N-phase Korteweg–deVries (KdV) wavetrains in the presence of external perturbations is investigated. An invariant representation of these modulation equations in terms of differentials on a Riemann surface is derived from averaged ...

For shallow caps under an axisymmetric external pressure distribution which is inward (with a representative magnitude $p_0 $) in a neighborhood of the pole and outward away from the pole, it has been shown previously that a finite axisymmetric dimple ...

Theoretical studies on flame stability have generally been based on one of two approaches: (i) the hydrodynamic model which accounts for thermal expansion due to combustion, but ignores flame structure, and (ii) the diffusional-thermal model which ...

We derive a nonlinear evolution equation and associated boundary conditions which, under certain circumstances, describe downward adiabatic flame propagation in long, vertical channels. We analyze this problem for the case of axial symmetry and show that ...

The diffusive Volterra equation with discrete or continuous delay is studied in the limit of long delays using matched asymptotic expansions. In the case of continuous delay, the procedure was explicitly carried out for general normalized kernels of the ...

A competition model involving two competing predator species and a single renewable resource prey species is studied under the assumption that the system parameters are periodic in time. It is shown by means of global bifurcation techniques that a ...

We present a formal perturbation expansion for the large scale effective drift velocity and diffusion matrix of a medium with stationary random velocity, $V(x)$, and constant nonrandom diffusion matrix, a, on a small scale. If $\mu $ denotes the mean of $...

The theory of best linear approximation in weighted $L^2 $ spaces is used to obtain a general procedure, the PDFT, for linearly reconstructing the Fourier transform from sampled data. The PDFT can be used either directly to reduce sidelobe structure and ...

The method of inclusion-exclusion can be used to obtain successive upper and lower bounds on the probability of the occurrence of complex events.

Usually only the first upper and the first lower bound are considered. But as they can be crude, further ...