Cauchy problem for effectiively hyperbolic operators with triple characteristics
Idioma
en
Article de revue
Este ítem está publicado en
Comptes rendus de l'Académie des sciences. Série I, Mathématique. 2014, vol. 352, p. 109-112
Elsevier
Resumen en inglés
We study a class of third-order effectively hyperbolic operators P in G = { x \in U, 0 \leq t \leq T} with triple characteristics at ρ = (0, x_0, ξ), ξ ∈ R^n \ {0}. V. Ivrii introduced the conjecture that every effectively ...Leer más >
We study a class of third-order effectively hyperbolic operators P in G = { x \in U, 0 \leq t \leq T} with triple characteristics at ρ = (0, x_0, ξ), ξ ∈ R^n \ {0}. V. Ivrii introduced the conjecture that every effectively hyperbolic operator is strongly hyperbolic, that is the Cauchy problem for P + Q is locally well posed for any lower-order terms Q . For operators with triple characteristics, this conjecture was established by Ivrii in the case when the principal symbol of P admits a factorization as a product of two symbols of principal type. A strongly hyperbolic operator in G could have triple characteristics in G only for t = 0 or for t = T . The operators that we investigate have a principal symbol which in general is not factorizable and we prove that these operators are strongly hyperbolic if T is small enough.< Leer menos
Orígen
Importado de HalCentros de investigación