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

  • T. Kenzizi

Abstract

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 $0<\alpha<\min(2,d),$ $(-\triangle)^{\frac{\alpha}{2}}$ is the fractional Laplacian on $\mathbb{R}^{d}$ and $\mathbb{R}^{d}$ and $u_{0}\in L^{2}(\mathbb{R}^{d}).$
Published
25.08.2019
How to Cite
KenziziT. “Existence of Nonnegative Solutions for a Fractional Parabolic Equation in the whole space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 8, Aug. 2019, pp. 1064-72, http://umj.imath.kiev.ua/index.php/umj/article/view/1498.
Section
Research articles