Decay estimates for evolutionary equations with fractional time-diffusion

Abstract

We consider an evolution equation whose time-diffusion is of fractional type, and we provide decay estimates in time for the \(L^s\)-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and comprises classical local and nonlocal diffusion equations.

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Correspondence to Serena Dipierro.

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This work has been carried out during a very pleasant visit of the third author at the School of Mathematics and Statistics at the University of Melbourne. Supported by the Australian Research Council Discovery Project Grant “N.E.W. Nonlocal Equations at Work” and by the G.N.A.M.P.A. Project “Nonlocal and degenerate problems in the Euclidean space.” The authors are members of G.N.A.M.P.A.–I.N.d.A.M.

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Dipierro, S., Valdinoci, E. & Vespri, V. Decay estimates for evolutionary equations with fractional time-diffusion. J. Evol. Equ. 19, 435–462 (2019). https://doi.org/10.1007/s00028-019-00482-z

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Keywords

  • Fractional diffusion
  • Parabolic equations
  • Decay of solutions in time with respect to Lebesgue norms

Mathematics Subject Classification

  • 26A33
  • 34A08
  • 35K90
  • 47J35
  • 58D25