Finite time extinction for nonlinear fractional evolution equations and related properties

Electronic Journal of Differential Equations

卷:2016

Teresa Pierantozzi¹  Jesus Ildefonso Diaz²  Luis Vazquez² 

[1]Barclays, UK

[2]|Univ. Complutense de Madrid, Spain

关键词: Nonlinear evolution equations;    fractional derivative;    finite time extinction;   

DOI  :  

来源: DOAJ

【 摘 要 】

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly,we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time.

【 授权许可】

Unknown