Solution of the Cauchy problem with values in refined spaces of Bessel potentials

• Date: 2015
• Main Authors: Lopushansky, A. O., Lopushanska, G. P., Лопушанський, А. О., Лопушанська, Г. П.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2015
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/198
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

For the Cauchy problem$$D^{\beta}_t u+a^2(-\Delta)^{\alpha/2}u=F_0(x,t),\;\;\; (x,t) \in \Bbb R^n\times (0,T],$$$$u(x,0)=F_{1}(x),\;\;\;x\in\Bbb R^n,$$with the regularized fractional derivative $D^{\beta}_t u$ of order $\beta\in (0,1)$, we establish the existence and uniqueness of the solutions that...