TY - JOUR
T1 - Hermitian Spectral Theory and Blow-Up Patterns for a Fourth-Order Semilinear Boussinesq Equation
AU - Galaktionov, V A
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=55649110251&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1111/j.1467-9590.2008.00421.x
U2 - 10.1111/j.1467-9590.2008.00421.x
DO - 10.1111/j.1467-9590.2008.00421.x
M3 - Article
VL - 121
SP - 395
EP - 431
JO - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
SN - 0022-2526
IS - 4
ER -