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

Elisa Affili, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)4027-4060
Number of pages34
JournalJournal of Differential Equations
Issue number7
Publication statusPublished - 15 Mar 2019


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