Lp-estimates for nonlocal in time heat kernels

Abstract: 

In [1] and [2], the authors study independently the so called fully nonlocal diffusion equation, which is of fractional order both in space and time. In both papers, the authors need several technical results about the so-called Mittag-Leffler functions and Fox H-functions to obtain Lp-estimates of the solutions. This approach seems not to be very helpful (or easy) to derive the Lp-estimates of solutions to equations with other nonlocal in time operators (for example sums of fractional derivatives). In this talk, we present a method to obtain Lp-estimates of fundamental solutions of more general nonlocal diffusion equations.

References
[1] K. Kim and S. Lim, Asymptotic behaviors of fundamental solution and its derivatives to frac- tional diffusion-wave equations, J. Korean Math. Soc. 53 (2016), no. 4, 929–967.
[2] J. Kemppainen, J. Siljander, and R. Zacher. Representation of solutions and large-time behavior for fully nonlocal diffusion equations. J. Differential Equations, 263(1):149-201, 2017.

Date: Jun 04, 2018 at 17:00 h
Venue: Sala de seminarios Felipe Álvarez Daziano, 5to. piso del DIM, U. de Chile, Torre Norte de Beauchef 851
Speaker: Juan Carlos Pozo
Affiliation: Universidad de la Frontera
Coordinator: Prof. Claudio Muñoz
Abstract:
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Posted on May 29, 2018 in CAPDE, Seminars