Well-posedness of the cauchy problem for complete second-order operator-differential equations

• Date: 1996
• Main Authors: Shklyar, A. Ya., Шкляр, А. Я.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5272
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the equation y″(t)+Ay′(t)+By(t)=0, where A and B are arbitrary commuting normal operators in a Hilbert space H, we obtain a necessary and sufficient condition for well-posedness of the Cauchy problem in the space of initial data D(B)×(D(A)∩D(|B|1/2)) and for weak well-posedness of the Cauchy pro...