B. D. Aggarwala

The logistic equation with a diffusionally coupled delay

Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Lyapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopfs bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.

Three collinear cracks in Plane elasticity and a related problem

We solve exactly a set of Quadruple Integral Equations containing Trigonometric Kernels and apply the solution to finding the shapes of three collinear cracks in Plane Elasticity, when the cracks are opened by constant internal pressure; and also to the problem of potential flow past three collinear plates. Numerical results are given.

Steady state temperatures in a quarter plane

The discontinuous boundary value problem of steady state temperatures in a quarter plane gives rise to a pair of dual integral equations which are not of Titchmarch type. These dual integral equations are considered in this paper.

On dual integral equations arising in problems of bending of anisotropic plates

In this paper we consider dual integral equations, which arise in boundary value problems of bending of anisotropic plates. The function involved in these equations is a linear combination of elementary function, which turns out to be a particular case of a class of Fourier kernels, [2]. The method used here for solving the equations is some what similar to the method used for solving dual integral equations of Titchmarsh type, [1].

Antibodies of HCV

We present a mathematical model which describes the development of HCV, and its resistant variants, in a patient. We assume that, apart from the variants that are already in the patient’s blood stream, it requires only one more mutation at a specific nucleotide for an HCV virus to become resistant to the antiviral drug being administered, i.e. for u 0 (virus, together with all its variants, present when the treatment starts) to change into u 1, virus which is resistant to the drug. We assume that, in the presence of drug pressure, it is easier for u 0, to change to u 1 than the other way around. The Model will say that there are exactly two outcomes of treatment: either the patient has a REBOUND of virus or SVR, sustained viral recovery. The model will also outline the important role of a patient’s immune system and say that if the immune system of the patient is strong enough, then HCV does not take hold. Finally, we shall also study how sensitive the results of our model are to changes in the treatment regime and/or to changes in the numerous parameters in the system.

ON QUADRUPLE INTEGRAL EQUATIONS INVOLVING TRIGONOMETRIC KERNELS

A general technique is developed for the solution of quadruple integral equations involving trigonometric kernels. Four such sets are solved explicitly. Application is made to the problem of three-collinear cracks in linear plane elasticity.

Fourier-like kernels as solutions of Ode's

In this paper, we generate asymmetric Fourier kernels as solutions of ODEs. These kernels give many previously known kernels as special cases. Several applications are considered.

Modified boundary integral method for pressure driven MHD duct flow

In this paper, ve investigate the flov of a viscous, Incompresslble, electrlcally conducting fluld through a rectangular duct in the presence of a magnetic fleld, when one of the boundaries perpedlcular to the umgnetlc field is partly conducting and partly Insu/atlng, by a modified Boundary Integral Hethod. Three problems are considered (1) flov through an infinite channel, (li) flov through a rectangular duct vhen the conducting part is symmetrlcally situated, and (Ill) flow through a rectangular duct vhen the conducting part is arbltrarily positioned. Such problems have been studied before by asyptotlc means for large values of H, the Hartmann nuaber. Hoverer, the present odlflcatlon of the Boundary Integral Method renders the proble coputatlonally efficient and provides a rellable ntmerlcal solutlon for all values of H. For large M, our coputatlon tlme decreases