Ukrainian Mathematical Journal ( IF 0.345 ) Pub Date : 2020-05-22 , DOI: 10.1007/s11253-020-01743-8
T. Kenzizi

The main aim of the present paper is to investigate the conditions under which the nonnegative solutions blow-up for the parabolic problem $$\frac{\partial u}{\partial t}=-{\left(-\Delta \right)}^{\frac{\alpha }{2}}u+\frac{c}{{\left|x\right|}^{\alpha }}u\kern1em \mathrm{in}\kern1em {\mathrm{\mathbb{R}}}^{\mathrm{d}}\times \left(0,T\right),$$ where 0 < α < min(2, d), $${\left(-\Delta \right)}^{\frac{\alpha }{2}}$$is the fractional Laplacian on ℝd and the initial condition u0 is in L2(ℝd).

down
wechat
bug