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Finite time extinction for nonlinear fractional evolution equations and related properties



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Díaz Díaz, Jesús Ildefonso and Pierantozzi, T.b and Vázquez, L. (2016) Finite time extinction for nonlinear fractional evolution equations and related properties. Electronic Journal of Differential Equations, 2016 (239). pp. 1-13. ISSN 10726691

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Official URL: http://ejde.math.txstate.edu/Volumes/2016/239/diaz.pdf


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. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Item Type:Article
Uncontrolled Keywords:Finite time extinction; Fractional derivative; Nonlinear evolution equations
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:39291
Deposited On:10 Oct 2016 12:24
Last Modified:12 Dec 2018 15:06

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