Slow Motion in Higher-Order Systems and -Convergence in One Space Dimension

We present a new variational approach for proving exponentially slow motion in singularly-perturbed partial differential equations in one space dimension, which builds on the energy approach due to Bronsard and Kohn (Comm. Pure Appl. Math. 43 (1990), pp. 983–997) and Grant (SIAM J. Math. Anal. 26 (1995), pp. 21–34). As well as covering the known applications, this approach is also capable of proving slow motion in equations whose corresponding Lyapunov functionals contain higher-order derivatives. Moreover, we obtain results on -convergence of these functionals. AMS subject classifications: 35B30, 35B25, 35K55