Decay estimates for time-fractional and other non-local in time subdiffusion equations in R^d
Kemppainen, J., Siljander, J., Vergara, V., & Zacher, R. (2016). Decay estimates for time-fractional and other non-local in time subdiffusion equations in R^d. Mathematische Annalen, 366(3), 941-979. https://doi.org/10.1007/s00208-015-1356-z
Julkaistu sarjassa
Mathematische AnnalenPäivämäärä
2016Tekijänoikeudet
© Springer-Verlag Berlin Heidelberg 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
We prove optimal estimates for the decay in time of solutions to a rather general class
of non-local in time subdiffusion equations in R
d
. An important special case is the timefractional
diffusion equation, which has seen much interest during the last years, mostly
due to its applications in the modeling of anomalous diffusion processes. We follow three
different approaches and techniques to study this particular case: (A) estimates based on
the fundamental solution and Young’s inequality, (B) Fourier multiplier methods, and (C)
the energy method. It turns out that the decay behaviour is markedly different from the
heat equation case, in particular there occurs a critical dimension phenomenon. The general
subdiffusion case is treated by method (B) and relies on a careful estimation of the underlying
relaxation function. Several examples of kernels, including the ultraslow diffusion case,
illustrate our results.
Julkaisija
SpringerISSN Hae Julkaisufoorumista
0025-5831Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/25458365
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
Kemppainen, Jukka; Siljander, Juhana; Zacher, Rico (Elsevier, 2017)We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay ... -
Spectral multipliers and wave equation for sub-Laplacians : lower regularity bounds of Euclidean type
Martini, Alessio; Müller, Detlef; Nicolussi Golo, Sebastiano (European Mathematical Society - EMS - Publishing House GmbH, 2023)Let L be a smooth second-order real differential operator in divergence form on a manifold of dimension n. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of ... -
The higher order fractional Calderón problem for linear local operators : Uniqueness
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther (Elsevier, 2022)We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that ... -
Spectroscopic studies of semiconducting single-walled carbon nanotubes
Siitonen, Anni (University of Jyväskylä, 2010)The unique nature of optical properties of single-walled carbon nanotubes (SWCNT), together with their promising potential applications, have created enormous interest towards the photophysics of SWCNT. Many aspects ... -
About time : A motivation-based complementary framework for temporal dynamics in Web personalization
Salonen, Ville; Karjaluoto, Heikki (Emerald Publishing Limited, 2019)
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.