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Long and Short Time Behavior of Non-local in Time Subdiffusion Equations

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Abstract

This paper is devoted to studying the long and short time behavior of the solutions to a class of non-local in time subdiffusion equations. To this end, we find sharp estimates of the fundamental solutions in Lebesgue spaces using tools of the theory of Volterra equations. Our results include, as particular cases, the so-called time-fractional and the ultraslow reaction-diffusion equations, which have seen much interest during the last years, mostly due to their applications in the modeling of anomalous diffusion processes.

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Acknowledgements

We would like to dedicate this paper to the memory of Professor Jan Prüss, whose significant contributions to the theory of evolution equations have been a constant inspiration for our work. Further, the second author had the privilege of being formed and collaborating with Jan, and his generosity of sharing ideas left a lasting impression on him. We would also like to thank the referee for the valuable comments, suggestions and corrections proposed in different parts of the document. These comments really enhanced the quality and presentation of our previous work.

Funding

The work of the Juan C. Pozo was partially supported by Chilean research grant of Fondo Nacional de Desarrollo Científico y Tecnológico, FONDECYT 1221271. The work of the Vicente Vergara was partially supported by Chilean research grant Fondo Nacional de Desarrollo Científico y Tecnológico, FONDECYT 1190255

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile

    Juan C. Pozo

  2. Departamento de Matemáticas, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Avenida Esteban Iturra s/n - Barrio Universitario - Casilla 160 C, Concepción, Chile

    Vicente Vergara

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  1. Juan C. Pozo
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Pozo, J.C., Vergara, V. Long and Short Time Behavior of Non-local in Time Subdiffusion Equations. Appl Math Optim 89, 50 (2024). https://doi.org/10.1007/s00245-024-10116-7

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