Seminari del Dipartimento di Matematica

Seminario del 2018

Vesselin Petkov

Cauchy problem for effectively hyperbolic operators with triple characteristics

analisi matematica

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.