Hermitian Spectral Theory and Blow-Up Patterns for a Fourth-Order Semilinear Boussinesq Equation

V A Galaktionov

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Two families of asymptotic blow-up patterns of nonsimilarity and similarity kinds are studied in the Cauchy problem for the fourth-order semilinear wave, or Boussinesq-type, equation The first countable family is constructed by matching with linearized patterns obtained via eigenfunctions (generalized Hermite polynomials) of a related quadratic pencil of linear operators. The second family comprises nonlinear blow-up patterns given by self-similar solutions. The results have their counterparts in the classic second-order semilinear wave equation which was known to admit blow-up solutions since Keller's work in 1957.
Original languageEnglish
Pages (from-to)395-431
Number of pages37
JournalStudies in Applied Mathematics
Volume121
Issue number4
DOIs
Publication statusPublished - 2008

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