2012

[93] J.C. Mattingly, N. Pillai and A.M. Stuart, Diffusion limits of the random walk Metropolis algorithm in high dimensions. Ann. Appl. Prob. 22 (2012) 881--930.
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[92] C. Schwab and A.M. Stuart, Sparse determinisitc approximation of Bayesian inverse problems. Inverse Problems. 28 (2012) 045003.
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[91] F.Pinski, A.M.Stuart and F. Theil, Gamma limit for transition paths of maximal probability. Journal of Statistical Physics. 146/5 (2012) 955-974.
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[90] S.L.Cotter, M. Dashti and A.M.Stuart, Variational data assimilation using targetted random walks. Int. J. Num. Meth. Fluids. 68(4) (2012) 403-421
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2011

[89] M.Dashti and A.M. Stuart, Uncertainty quantification and weak approximation of an elliptic inverse problem. SIAM J. Numerical Analysis 49(2011), 2524--2542.
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[88] W. Lee, D. McDougall and A.M. Stuart, Kalman filtering and smoothing for linear wave equations with model error. Inverse Problems. 27 (2011) 095008.
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[87] A. Beskos, F.J. Pinski, J.-M. Sanz-Serna and A.M. Stuart, Hybrid Monte-Carlo on Hilbert Spaces. Stochastic Processes and their Applications. 121 (2011) 2201-2230.
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[86] M. Hairer, A.M. Stuart and J. Voss, Sampling conditioned hypoelliptic diffusions. Annals of Applied Probability 21 (2011) 669-698.
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[85] I. Melbourne and A.M. Stuart,A note on diffusion limits of chaotic skew product flows. Nonlinearity 24 (2011) 1361-1367.
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2010

[84] P. Fearnhead, O. Papaspiliopoulos, G.O. Roberts and A.M. Stuart, Random-weight particle filtering of continuous time stochastic processes. Journal of the Royal Statistical Society B. 72(4) (2010) 497-512.
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[83] J.C. Mattingly, A.M. Stuart and M. Tretyakov, Convergence of numerical time-averaging and stationary measures via the Poisson equation. SIAM Journal of Numerical Analysis. 48(2) (2010) 552-577.
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[82] F.J. Pinski and A.M. Stuart, Transition paths in molecules: gradient descent in pathspace. Journal of Chemical Physics 132 (2010), 184104.
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[81] S.L. Cotter, M. Dashti and A.M. Stuart, Approximation of Bayesian Inverse Problems. SIAM Journal of Numerical Analysis 48 (2010) 322-345.
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2009

[80] S.L. Cotter, M. Dashti, J.C. Robinson and A.M. Stuart, Bayesian inverse problems for functions and applications to fluid mechanics. Inverse Problems 25 (2009) 115008. doi: 10.1088/0266-5611/25/11/115008.
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[79] Y. Pokern, A.M. Stuart and E. Vanden Eijnden, Remarks on drift estimation for diffusion processes. SIAM Multiscale Modelling and Simulation 8 (2009) 69-95. doi:10.1137/070694806.
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[78] A. Beskos, G.O. Roberts and A.M. Stuart, Optimal scalings of Metropolis-Hastings algorithms for non-product targets in high dimensions. Annals of Applied Probability 19 (2009) 863-898.
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[77] A. Papavasiliou, G. Pavliotis and A.M. Stuart, Maximum likelihood estimation for multiscale diffusions. Stochastic Processes and their Applications 19 (2009) 3173-3210.
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[76] Y. Pokern, A.M. Stuart and P. Wiberg, Parameter estimation for partially observed hypo-elliptic diffusions. Journal of the Royal Statistical Society B 71 (2009) 49-73.
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[75] G. Pavliotis, A.M. Stuart and K. Zygalakis, Calculating effective diffusivities in the limit of vanishing molecular diffusion. Journal of Computational Physics 228 (2009) 1030-1055.
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2008

[74] A. Beskos, G. Roberts, A.M. Stuart and J. Voss, An MCMC method for diffusion bridges. Stochastics and Dynamics 8 (2008) 319-350.
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[73] A. Apte, C.K.R.T. Jones, A.M. Stuart and J. Voss, Data assimilation: mathematical and statistical perspectives. International Journal of Numerical Methods in Fluids 56 (2008) 1033-1046.
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[72] A. Apte, C.K.R.T. Jones and A.M. Stuart, A Bayesian approach to Lagrangian data assimilation. Tellus A 60 (2008) 336-347.
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2007

[71] G. Pavliotis, A.M. Stuart and K. Zygalakis, Homogenization for inertial particles in a random flow. Communications in Mathematical Sciences 5 (2007) 507-531.
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[70] M. Hairer, A.M. Stuart and J. Voss, Analysis of SPDEs arising in path sampling part II: the nonlinear case. Annals of Applied Probability 17(5-6) (Oct 2007) 1657-1706.
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[69] G. Pavliotis and A.M. Stuart, Parameter estimation for multiscale diffusions. Journal of Statistical Physics 127 (2007) 741-781.
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[68] A. Apte, M. Hairer, A.M. Stuart and J. Voss, A Bayesian approach to data assimilation. Physica D Nonlinear Phenomena 230 (2007) 50-64.
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[67] H. Lamba, J.C. Mattingly and A.M. Stuart, An adaptive Euler-Maruyama scheme for SDEs: convergence and stability. IMA Journal of Numerical Analysis 27 (2007) 479-506.
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2006

[66] D. Barkley, I.G. Kevrekidis and A.M. Stuart, The moment map: nonlinear dynamics of density evolution via a few moments. SIAM Journal of Applied Dynamical Systems 5 (2006) 403-434.
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2005

[65] M. Hairer, A.M. Stuart, J. Voss and P. Wiberg, Analysis of SPDEs arising in path sampling part I: the Gaussian case. Communications in Mathematical Sciences 3(4) (2005) 587-603.
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[64] G.A. Pavliotis and A.M. Stuart, Periodic homogenization for inertial particles. Physica D Nonlinear Phenomena 204 (2005) 161-187.
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[63] G. Pavliotis and A.M. Stuart, Analysis of white noise limits for stochastic systems with two fast relaxation times. SIAM Multiscale Modelling and Simulation 4 (2005) 1-35.
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2004

[62] R. Kupferman and A.M. Stuart, Fitting SDE models to nonlinear Kac-Zwanzig heat bath models. Physica D Nonlinear Phenomena 199 (2004) 279-316.
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[61] A.M. Stuart, P. Wiberg and J. Voss, Conditional path sampling of SDEs and the Langevin MCMC method. Communications in Mathematical Sciences 2(4) (Dec 2004) 685-697.
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[60] R. Kupferman, G. Pavliotis and A.M. Stuart, Ito versus Stratonovich white noise limits for systems with inertia and colored multiplicative noise. Physical Review E 70 (2004) 036120.
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[59] D. Givon, R. Kupferman, and A.M. Stuart, Extracting macroscopic dynamics: model problems and algorithms. Nonlinearity 17 (2004) 55-127.
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2003

[58] D.J. Higham, X. Mao and A.M. Stuart, Mean square stability of numerical solutions to stochastic differential equations. LMS Journal of Computational Mathematics 6 (2003) 297-313.
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[57] G. Pavliotis and A.M. Stuart, White noise limits for inertial particles in a random field. SIAM Multiscale Modelling and Simulation 1 (2003) 527-553.
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[56] W. Husinga, C. Schutte and A.M. Stuart, Extracting macroscopic stochastic models from dynamics. Communications in Pure and Applied Mathematics LVI (2003) 234-269.
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2002

[55] H. Sigurgeirsson and A.M. Stuart, A model for preferential concentration. Physics of Fluids 14 (2002) 4352-4361.
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[54] H. Sigurgeirsson and A.M. Stuart, Inertial particles in a random field. Stochastics and Dynamics 2 (2002) 295-310.
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[53] R. Kupferman, A.M. Stuart, J. Terry and P. Tupper, Long time behaviour of large mechanical systems with random initial data. Stochastics and Dynamics 2 (2002) 533-562.
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[52] J. Mattingly and A.M. Stuart, Geometric ergodicity of some hypo-elliptic diffusions for particle motions. Markov Processes and Related Fields 8 (2002) 199-214.
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[51] D.J. Higham, X. Mao and A.M. Stuart, Strong convergence of Euler type methods for nonlinear stochastic differential equations. SIAM Journal of Numerical Analysis 40(3) (Aug 2002) 1041-1063. 10.1137/S0036142901389530
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[50] J. Mattingly, A.M. Stuart and D.J. Higham, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Stochastic Processes and their Applications 101(2) (Oct 2002) 185-232. 10.1016/S0304-4149(02)00150-3
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[49] D.J. Estep and A.M. Stuart, The dynamical behaviour of the discontinuous Galerkin method and related difference schemes. Mathematics of Computation 71 (2002) 1075-1103.
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2001

[48] H. Sigurgeirsson, A.M. Stuart and J. Wan, Algorithms for Particle-Field Simulations with Collisions. J. Comp. Phys. 172 (2001),766-807.
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[47] B. Cano and A.M. Stuart, Under-resolved simulations of heat baths. J. Comp. Phys. 169 (2001) 193-214.
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[46] B. Cano, E. Suli, A.M. Stuart and J. Warren, Stiff oscillatory systems, delta jumps and white noise. Found. Comp. Math. 1 (2001) 69-100.
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2000

[45] T. Shardlow and A.M. Stuart, A perturbation theory for ergodic Markov chains with application to numerical approximation. SIAM J. Num. Anal. 37 (2000) 1120-1137.
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1999

[44] A.M. Stuart and J. Warren, Analysis and experiments for a computational model of a heat bath. J. Stat. Phys. 97 (1999) 687-723.
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[43] O. Gonzalez, D.J. Higham and A.M. Stuart, On the qualitative properties of modified equations. IMA J. Num. Anal. 19 (1999) 169-190.
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[42] J.M. Sanz-Serna and A.M. Stuart, Ergodic Properties of Dissipative Differential Equations Subject to Random Impulses. J. Diff. Eq., 155 (1999) 262-284.
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1998

[41] H. Lamba and A.M. Stuart, Convergence Results for the MATLAB ode23 Routine. BIT 38 (1998), 751-780.
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[40] D.A. Jones, A.M. Stuart and E.S. Titi, Persistence of Invariant Sets for Dissipative Evolution Equations. J. Math. Anal. and Applic. 219 (1998), 479-502.
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[39] M. Gander and A.M. Stuart, Parallel Algorithms for the Solution of Time-Dependent Partial Differential Equations. SIAM J. Sci. Comp. 19 (1998), 2014-2031.
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[38] C.J. Budd, G.P. Koomullil and A.M. Stuart, On the solution of convection-diffusion boundary-value problems by grid adaptation. SIAM J. Sci. Stat. Comp. 20 (1998), 591-618.
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[37] D.J. Higham and A.M. Stuart, Analysis of the dynamics of error control via a piecewise continuous residual. BIT 38 (1998), 44-57.
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1997

[36] A.M. Stuart, Probabilistic and Deterministic Convergence Proofs for Software for Initial Value Problems. Numerical Algorithms 14 (1997) 227-260.
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[35] M. Bjorhus and A.M. Stuart, Waveform relaxation as a dynamical system. Math. Comp. 66 (1997) 1101-1117.
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1996

[34] C.M. Elliott and A.M. Stuart, The viscous Cahn-Hilliard equation. Part II: Analysis. J. Diff. Equations. 128 (1996) 387-414.
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1995

[33] D.A. Jones and A.M. Stuart, Attractive Invariant Manifolds Under Approximation. Part I: Inertial Manifolds. J. Diff. Eq. 123 (1995) 588-637.
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[32] A.M. Stuart and A.R. Humphries, The Essential Stability of Local Error Control for Dissipative and Gradient Dynamical Systems. SIAM J. Num. Anal. 32 (1995) 1940-1971.
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[31] G.J. Lord and A.M. Stuart, Gevrey regularity and upper semicontinuity of attractors for a semi-discrete Ginzburg-Landau equation. Num. Func. Anal. Appl. 16 (1995) 1003-1047.
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[30] D.J. Estep and A.M. Stuart, The rate of error growth in Hamiltonian conserving integrators. ZAMP 46 (1995) 407-418.
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[29] F. Bai, C.M. Elliott, A. Gardiner, A. Spence and A.M. Stuart, The viscous Cahn- Hilliard equation. Part I: Computations. Nonlinearity 8 (1995) 131-160.
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1994

[28] F. Bai, A. Spence and A.M. Stuart, Numerical Computations of Coarsening in the Cahn-Hilliard model of phase separation. Physica D. 78 (1994), 155-165.
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[27] A.M. Stuart and A.R. Humphries, Model Problems in Numerical Stability for Initial Value Problems. SIAM Review 36 (1994), 226-257.
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[26] A.R. Humphries and A.M. Stuart, Runge-Kutta methods for dissipative and gradient dynamical systems. SIAM J. Num. Anal. 31 (1994), 1452-1485.
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[25] C.J. Budd, J.W. Dold and A.M. Stuart, The study of blow-up in a system of partial differential equations with conserved first integral. Part II: Non-zero convection. SIAM J. Appl. Math. 54 (1994) 610-640.
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1993

[24] F. Bai, A. Spence and A.M. Stuart, The Numerical Computation of Heteroclinic Connections in Systems of Gradient Partial Differential Equations. SIAM J. Appl. Math. 35 (1993) 743-769.
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[23] C.J. Budd, J.W. Dold and A.M. Stuart, The study of blow-up in a system of partial differential equations with conserved first integral. Part I: Zero convection. SIAM J. Appl. Math. 53 (1993) 718-742.
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[22] C.M. Elliott and A.M. Stuart, The global dynamics of discrete semilinear parabolic equations. SIAM J. Num. Anal. 30 (1993) 1622-1663.
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[21] M.A.J. Chaplain and A.M. Stuart, A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. IMA J. Math. Appl. Med. Biol. 10 (1993), 149-168.
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1992

[20] J.M. Sanz-Serna and A.M. Stuart, A note on uniform in time error estimates for reaction-diffusion equations. IMA J. Num. Anal. 12 (1992) 457-462.
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[19] D.F. Griffiths, A.M. Stuart and H.C. Yee, Numerical wave propagation in hyperbolic equations with source terms. SIAM J. Num. Anal. 29 (1992) 1244-1260.
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[18] A. Iserles and A.M. Stuart, A unified approach to spurious solutions introduced by timediscretisation. Part II. BDF-like methods. IMA J. Num. Anal. 12 (1992) 487-502.
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1991

[17] M.A.J. Chaplain and A.M. Stuart, A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue. IMA J. Math. Appl. Med. Biol. 8 (1991) 191-220.
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[16] A. Iserles, A.T. Peplow and A.M. Stuart, A unified approach to spurious solutions introduced by time-discretisation. Part I Basic Theory. SIAM J. Num. Anal. 28 (1991) 1723-1751.
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[15] A.M. Stuart and A.T. Peplow, The dynamics of the theta method. SIAM J. Sci. Stat. Comp. 12 (1991) 1351-1372.
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[14] A.M. Stuart, Singular Limits In Free Boundary Problems. Rocky Mountain J. Math. 21 (1991) 809-811.
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1990

[13] A.M. Stuart and M.S. Floater, On the Computation of Blow-up. Euro. J. Appl. Math. 1 (1990) 47-71.
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1989

[12] A.M. Stuart, Linear Instability Implies Spurious Periodic Solutions. IMA J. Num. Anal. 9 (1989)465-486.
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[11] J. Norbury and A.M. Stuart, A Model For Porous Medium Combustion. Quart. J. Mech. Appl. Math. 42 (1989)159-178.
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[10] A.M. Stuart, A Note On High/Low Wave Number Interactions In Spatially Discrete Parabolic Equations. IMA J. Appl. Math. 42 (1989) 27-42.
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[9] A.M. Stuart, Nonlinear Instability In Dissipative Finite Difference Schemes. SIAM Review 31 (1989) 191-220.
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[8] A.M. Stuart, Singular Free Boundary Problems And Local Bifurcation Theory. SIAM J. Appl. Math. 49 (1989) 72-85.
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1988

[7] A.M. Stuart, Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity. IMA J. Appl. Math. 40 (1988) 217-234.
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[6] J. Norbury and A.M. Stuart, Parabolic Free Boundary Problems Arising in Porous Medium Combustion. IMA J. Appl. Math. 39 (1988) 241-257.
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[5] J. Norbury and A.M. Stuart, Travelling Combustion Waves in a Porous Medium. Part II — Stability. SIAM J. Appl. Math. 48 (1988) 374-392.
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[4] J. Norbury and A.M. Stuart, Travelling Combustion Waves in a Porous Medium. Part I — Existence. SIAM J. Appl. Math. 48 (1988) 155-169.
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1987

[3] A.M. Stuart, Existence of Solutions of a Two-Point Free Boundary Problem Arising in the Theory of Porous Medium Combustion. IMA J. Appl. Math. 38 (1987) 23-34.
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[2] J. Norbury and A.M. Stuart, Volterra Integral Equations and a New Gronwall Inequality. Part II: The Nonlinear Case. Proc. Roy. Soc. Edin. 106A (1987) 375-384.
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[1] J. Norbury and A.M. Stuart, Volterra Integral Equations and a New Gronwall Inequality. Part I: The Linear Case. Proc. Roy. Soc. Edin. 106A (1987) 361-373.
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