Existence results for  nonlinear  mono-energetic singular transport equations: $ L^p $-spaces

Khalid Latrach; Hssaine Oummi; Ahmed Zeghal

doi:10.3934/dcdss.2021028

Article Contents

2022, Volume 15, Issue 1: 179-195. Doi: 10.3934/dcdss.2021028

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Existence results for nonlinear mono-energetic singular transport equations: $ L^p $-spaces

1.
Université Clermont Auvergne CNRS, LMBP F-63000 Clermont-Ferrand, France
2.
Université Sultan Moulay Slimane, Faculté des Sciences et Techniques, Laboratoire de Mathématiques et Applications, B.P. 523, 23000 Beni-Mellal, Morocco
3.
Université Abdelmalek Essâadi, Faculté des Sciences et Techniques, Laboratoire de Mathématiques et Applications, B.P. 416, 90000 Tangier, Morocco

^* Corresponding author: Ahmed Zeghal (azeghal@uae.ac.ma)
^* Corresponding author: Ahmed Zeghal (azeghal@uae.ac.ma)

Received: July 31, 2020

Revised: December 31, 2020

Early access: March 2021

Published: January 2022

The second author is supported by CNRST grant 18USMS2016

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Abstract

We establish some results regarding the existence of solutions to a nonlinear mono-energetic singular transport equation in slab geometry on $ L^p $-spaces with $ p\in (1,+\infty) $. Both the cases where the boundary conditions are specular reflections and periodic are discussed.

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Mathematics Subject Classification: 35F20, 45K05, 45P05, 47H10.

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