References
J. S. Langer, Existence of needle crystals in local models of solidification, Phys. Rev. A 33 (1986), 435–441.
M. D. Kruskal & H. Segur, Asymptotics beyond all orders in a model of crystal growth, preprint.
J. Hammersley & G. Mazzarino, A differential equation connected with the dendritic growth of crystals, IMA J. Appl. Math. 42 (1989), 43–75.
J. F. Toland, Existence and uniqueness of heteroclinic orbits for the equation λu‴+u′=f(u), Proc. Royal Soc. Edin. 109 A (1988), 23–36.
W. C. Troy, Nonexistence of monotonic solutions in a model of dendritic growth, preprint.
D. Michelson, Steady solutions of the Kuramoto-Sivashinsky equation, Physica D 19 (1986), 89–111.
J. G. B. Byatt-Smith, The asymptotic solution of a connection problem of a second order ordinary differential equation, preprint.
C. J. Amick & K. Kirchgässner, A theory of solitary water-waves in the presence of surface tension, Arch. Rational Mech. Anal. 105 (1988), 1–50.
J. K. Hunter & J. K. Scheurle, Existence of perturbed solitary wave solutions to a model equation for water waves, Physica D, to appear.
C. J. Amick & J. B. McLeod, A singular perturbation problem in water waves, to appear.
C. J. Amick & J. F. Toland, A differential equation in the theory of resonant oscillations of water waves, Proc. Royal Soc. Edin., to appear.
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Amick, C.J., McLeod, J.B. A singular perturbation problem in needle crystals. Arch. Rational Mech. Anal. 109, 139–171 (1990). https://doi.org/10.1007/BF00405240
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DOI: https://doi.org/10.1007/BF00405240