Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.

Decay estimates for evolution equations with classical and fractional time-derivatives / E. Affili, E. Valdinoci. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 266:7(2019 Mar 15), pp. 4027-4060. [10.1016/j.jde.2018.09.031]

Decay estimates for evolution equations with classical and fractional time-derivatives

E. Affili
Primo
;
E. Valdinoci
Ultimo
2019

Abstract

Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.
fractional derivatives; fractional PDEs; decay estimates;
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/820879
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