Radon measure-valued solutions of unsteady filtration equations

Maria Michaela Porzio; Flavia Smarrazzo; Alberto Tesei

doi:10.3934/dcds.2022040

Article Contents

2023, Volume 43, Issue 3&4: 1595-1624. Doi: 10.3934/dcds.2022040

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Radon measure-valued solutions of unsteady filtration equations

1.
Dipartimento di Pianificazione, Design, Tecnologie dell'Architettura, Università Sapienza di Roma, via Flaminia 70, 00196 Roma, Italy
2.
Università Campus Bio-Medico di Roma, Via Alvaro del Portillo 21, 00128 Roma, Italy
3.
Dipartimento di Matematica "G. Castelnuovo", Università Sapienza di Roma, P.le A. Moro 5, I-00185 Roma
4.
Istituto per le Applicazioni del Calcolo "M. Picone", CNR, Roma, Italy

^*Corresponding author: Alberto Tesei
^*Corresponding author: Alberto Tesei

Received: November 2021

Revised: February 2022

Early access: April 2022

Published: March 2023

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Abstract

We study Radon measure-valued solutions of a Cauchy-Dirichlet problem in one space dimension that describes nonlinear convection-diffusion phenomena in heterogeneous media. Well-posedness results are proven, which extend those previously known for the space homogeneous case.

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Mathematics Subject Classification: Primary: 35K59, 35D99, 35R06; Secondary: 35Q35, 28A33.

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References

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