Variational Approach to Complicated Similarity Solutions of Higher-Order   Nonlinear PDEs. II
  Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of compactly supported solutions. 
V.A. Galaktionov, E. Mitidieri, and S.I. Pohozaev
math.AP