Existence of nonnegative solutions for a fractional parabolic equation in the whole space

• Date: 2019
• Main Authors: Kenzizi, T., Кензізі, Т.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1498
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 We study existence of nonnegative solutions for a parabolic problem $\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ in $\mathbb{R}^{d}\times (0, T).$ Here $0