Complexity of asymptotic behavior of solutions for the fractional porous medium equation
Complexity of asymptotic behavior of solutions for the fractional porous medium equation
In this paper, we study the large time behavior of solutions to the fractional porous medium equation $ u_{t} = \nabla\cdot (u\nabla^{\alpha-1}u) $ in $ \mathbb{R}^{N} $ with $ 0<\alpha<2 $. More precisely, we reveal that for any given $ 0<\mu<\frac{2N}{N+\alpha} $ and $ \beta>\frac{2-\mu}{2\alpha} $, there exists an initial-value …