Open AccessInhomogeneous Gevrey ultradistributions and Cauchy problem
Author(s) -
D. Calvo,
Luigi Rodino
Publication year - 2006
Publication title -
bulletin - académie serbe des sciences et des arts. classe des sciences mathématiques et naturelles. sciences mathématiques/bulletin
Language(s) - English
Resource type - Journals
eISSN - 2406-0909
pISSN - 0561-7332
DOI - 10.2298/bmat0631176c
Subject(s) - mathematics , homogeneous , initial value problem , frame (networking) , cauchy distribution , differential operator , function (biology) , cauchy problem , mathematical analysis , hyperbolic partial differential equation , pure mathematics , partial differential equation , computer science , combinatorics , telecommunications , evolutionary biology , biology
After a short survey on Gevrey functions and ultradistributions, we present the inhomogeneous Gevrey ultradistributions introduced recently by the authors in collaboration with A. Morando, cf. [7]. Their definition depends on a given weight function ?, satisfying suitable hypotheses, according to Liess-Rodino [16]. As an application, we define (s, ?)-hyperbolic partial differential operators with constant coefficients (for s > 1), and prove for them the well-posedness of the Cauchy problem in the frame of the corresponding inhomogeneous ultradistributions. This sets in the dual spaces a similar result of Calvo [4] in the inhomogeneous Gevrey classes, that in turn extends a previous result of Larsson [14] for weakly hyperbolic operators in standard homogeneous Gevrey classes. AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.