Seminario di analisi matematica
ore
11:15
presso - Aula Da Stabilire -
We consider the Cauchy problem for hyperbolic operators with characteristics
of variable multiplicities r ≤ 3 assuming that the fundamental matrix of the principal sym-
bol has two non-vanishing real eigenvalues. The last condition is necessary for the Cauchy
problem to be well posed for every choice of lower order terms. The operators with this pro-
perty are called strongly hyperbolic and it was conjectured that every effectively hyperbolic
operator is strongly hyperbolic. In this talk we present a survey of the results in the case
r = 3. The proofs are based on the energy estimates with a big loss of derivatives depending
of lower order terms. This is a joint work with T. Nishitani.