Between 1994 and 2002 the Department published an Applied Mathematics reports series listed below. This series has now been subsumed into the Preprint series and the Mathematics Report series.

### 2002

2002/1 The effect of evanescent wave modes on scattering and near trapping

P.G. Chamberlain

### 2001

2001/1 Wave scattering by a perforated duct

N R T Biggs & D Porter

2001/2 The evolution of travelling waves in generalised Fisher equations via

matched asymptotic expansions: exponential corrections

J.A.Leach and D.J.Needham

2001/3 Scattered & free waves over periodic beds.

R Porter & D Porter

### 2000

2000/1 The evolution of reaction-diffusion waves in a class of scalar reaction-diffusion equations: algebraic decay rates

J.A.Leach and D.J.Needham

2000/2 Interaction of water waves with three-dimensional periodic topographs.

R. Porter and D. Porter

2000/3 Wave diffraction through a perforated barrier of non-zero thickness.

N R T Biggs & D Porter

2000/4 The evolution of travelling waves in the weakly hyperbolic genralised

Fisher Model

D J Needham & A C King

### 1999

99/1 The evolution of travelling waves in fractional order autocatalysis with decay. III. The coupled system.

P.M.McCabe, J.A.Leach and D.J.Needham

99/2 The evolution of travelling waves in generalized Fisher equations via matched asymptotic expansions.

J.A.Leach and D.J.Needham

### 1998

98/1 Scattering and near-trapping of water waves by axi-symmetric topography.

P.G.Chamberlain and D.Porter

98/3 The evolution of travelling waves in fractional order autocatalysis with decay. II. The initial boundary value problem.

P.M.McCabe, J.A.Leach and D.J.Needham

### 1997

97/1 Propagating interfaces in a reaction-diffusion model with species immobilization. I. Simultaneous immobilization.

D.J. Needham, A.C. King and J.H. Merkin

97/2 Centre families in two-dimensional complex holomorphic dynamical systems.

D.J. Needham and S. McAllister

97/3 Topographical scattering of gravity waves

J.W. Miles and P.G. Chamberlain

### 1996

96/1 Approximations to wave trapping by topography.

P.G. Chamberlain and D. Porter

96/2 Global similarity solutions to a class of semilinear parabolic equations: existence, bifurcations and asymptotics.

D.J. Needham and P.G. Chamberlain

96/3 The effects of weak hyperbolicity on the diffusion of heat.

A.C. King, D.J. Needham and N.H. Scott

96/4 The evolution of travelling waves in fractional order autocatalysis with decay. I. Permanent form travelling waves.

P.M. McCabe, J.A. Leach and D.J. Needham

### 1995

95/1 A reaction diffusion model for autocatalytic polymerization. The initial value problem.

D.J. Needham, A.C. King and J.H. Merkin

95/2 A reaction-diffusion model for autocatalytic polymerization.

D.J. Needham, A.C. King and J.H. Merkin

95/3 Linear wave scattering by two-dimensional topography.

D. Porter and P.G. Chamberlain

95/4 Extensions of the mild-slope equations.

D. Porter and D.J. Staziker

95/5 On simple waves and weak shock theory for the equations of alluvial river hydraulics.

D.D.L. Zanre and D.J. Needham

95/6 The scattering of surface waves by local bed elevations.

D.J. Staziker, D. Porter and D.S.G. Stirling

95/7 On the alluvial hydraulics of steady flow around a bridge pier.

D.J. Needham and D.D.L. Zanre

### 1994

94/1 The modified mild-slope equation

P.G. Chamberlain and D. Porter

94/2 Decomposition methods for wave scattering by topography with application to ripple beds

P.G. Chamberlain and D. Porter

94/3 A centre theorem for two-dimensional complex holomorphic systems and its generalization

D.J. Needham

94/4 The effects of coupling on chemical wave propagation in quadratic and cubic autocatalysis with decay

D.J. Needham and J.H. Merkin

94/5 The propagation of reaction-diffusion waves in coupled autocatalytic systems

J.H. Merkin, M.J. Metcalf, D.J. Needham and S.K. Scott

94/6 Stable pattern and standing wave formation in a simple isothermal cubic autocatalytic reaction scheme

R. Hill, J.H. Merkin and D.J. Needham