In this paper, we study the initial boundary value problem of space-fractional diffusion equations. First, we introduce a family of potential wells. Then we show the existence of global weak solutions, provided that the initial energy is positive and less than the potential well depth d. Finally, we establish the vacuum isolating and blow up of strong solutions.
On solutions of space–fractional diffusion equations by means of potential wells
PUCCI, Patrizia
2016
Abstract
In this paper, we study the initial boundary value problem of space-fractional diffusion equations. First, we introduce a family of potential wells. Then we show the existence of global weak solutions, provided that the initial energy is positive and less than the potential well depth d. Finally, we establish the vacuum isolating and blow up of strong solutions.File in questo prodotto:
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