References for Math 238, Topics in Nonlinear PDE

  • Analysis of Partial Differential Equations, Elementary texts:

    (1) L. C. Evans, Partial Differential Equations, American Mathematical Society, 1998.
    (2) G. B. Folland Introduction to Partial Differential Equations, Princeton University Press, 1976. There is a newer edition.
    (3) F. John Partial Differential Equations, Springer-Verlag, 1982.

  • More advance analysis texts:

    (1) M. Taylor Partial Differential Equations vols I, II, and III. Springer Applied Mathematical Sciences vol 117
    (2) L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, AMS CMBS Series number 74, 1988.
    (3) A. J. Majda and A. L. Bertozzi Vorticity and Incompressible Flow, Cambridge Univ. Press, 2001 (in press).

  • Pattern formation and bifurcations

    (1) Dieter Armbruster, John Guckenheimer, and Philip Holmes, "Kuramoto-Sivashinsky dynamics on the center-unstable manifold", SIAM J. Appl. Math., 49, pp. 676-691, 1989.
    (2) John Guckenheimer and Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , Springer-Verlag, 1983.
    (3) M. Cross and P. C. Hohenberg, Pattern Formation Oustide of Equilibrium

  • Self-similarity

    (1) Barenblatt, Scaling, self-similarity, and intermediate asymptotics, Cambridge Univ. Press, 1996.