Recent Papers (1999- )

1. P.M.McCabe, J.A.Leach and D.J.Needham. The evolution of travelling waves in fractional order autocatalysis with decay. I. Permanent form travelling waves.
   SIAM J. Appl. Math. Vol.59, No.3 (1999) 870-899. Abstract
   
2. P.M.McCabe, J.A.Leach and D.J.Needham. The evolution of travelling waves in fractional order autocatalysis with decay. II. The initial boundary value problem.
   SIAM J. Appl. Math. Vol.60, No.5 (2000) 1707-1748.
3. J.A.Leach and D.J.Needham. The evolution of travelling waves in generalized Fisher equations via matched asymptotic expansions. I Algebraic Corrections.
   Q.Jl Mech. Appl. Math. 54 (1) (2001) 157-175.
4. P.M.McCabe, J.A.Leach and D.J.Needham. A note on the non-existence of permanent form travelling wave solutions in a class of singular reaction-diffusion problems.
   Dynamical Systems, Vol. 17, No. 2, (2002) 131-135.
   
5. J.A.Leach and D.J.Needham. The evolution of reaction-diffusion waves in a class of scalar reaction-diffusion equations: Algebraic decay rates.
   Physica D, Nonlinear Phenomena, 167 (3-4) (2002) 153-182.

6. J.A.Leach and D.J.Needham. A review of the evolution of reaction-diffusion waves in a class of scalar reaction-diffusion equations.
   International Journal of Differential Equations and Applications, Vol. 5 No. 2 (2002) 159-169.
7. P.M.McCabe, J.A.Leach and D.J.Needham. On an initial-boundary-value problem for a coupled, singular reaction-diffusion system arising from a model of fractional order chemical autocatalysis with decay.
   Q. Jl Mech. Appl. Math. 50 (4) (2002) 511-560
8. A.L.Kay, D.J. Needham and J.A. Leach. Travelling waves in a simple chemical system with fractional order autocatalysis and decay: Comparison to orders above unity.
   Dynamics of Continuous, Discrete and Impulsive Sytems, Ser. B, Vol. 10, No. 3 (2003) 455-468.
9. J.A. Leach, D.J. Needham and A.L.Kay. The evolution of reaction-diffusion waves in generalized Fisher equations: Exponential decay rates.
   Dynamics of Continuous, Discrete and Impulsive Sytems, Ser. A, Vol. 10, No. 3 (2003) 417-430.
10. J.A. Leach, D.J. Needham and A.L.Kay. The evolution of reaction-diffusion waves in a class of scalar reaction-diffusion equations: Initial data with compact support and exponential decay rates.
    Q.Jl Mech. Appl. Math. 56 (2) (2003) 217-249.
11. A.L.Kay, D.J. Needham and J.A. Leach. Travelling waves for a coupled, singular reaction-diffusion system arising from a model of fractional order autocatalysis with decay.
    Nonlinearity Vol. 16, No. 2 (2003) 735-770.
12. J.A.Leach and D.J.Needham. The evolution of travelling waves in generalized Fisher equations via matched asymptotic expansions: Exponential Corrections. (To appear: ZAMP)
13. J.A.Leach and J.C.Wei. Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I Stability analysis.
    Physica D, Nonlinear Phenomena, 180 (3-4) (2003) 217-249.
14. P.M.McCabe, J.A.Leach and D.J.Needham. The evolution of travelling waves in fractional order autocatalysis with decay: Algebraic and exponential decay rates. (To appear: ZAMP)

Recent Submissions

1. S.C.Smith, D.J.Needham and J.A.Leach. The evolution of travelling waves in a simple model for an ionic autocatalytic system. (Submitted to: Proc. Roy. Soc. Lond. Ser. A)

In Preparation

1. J.A.Leach and J.C.Wei. Pattern formation in a simple chemical system with general orders of autocatalysis and decay. II Asymptotic analysis.

2. J.A. Leach, D.J. Needham and K.W.Blake. A note on the evolution of accelerating phase waves in a class of nonlinear diffusion equations.