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

Abstract

<p style='text-indent:20px;'>We establish some results regarding the existence of solutions to a nonlinear mono-energetic singular transport equation in slab geometry on <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-spaces with <inline-formula><tex-math id="M3">\begin{document}$ p\in (1,+\infty) $\end{document}</tex-math></inline-formula>. Both the cases where the boundary conditions are specular reflections and periodic are discussed.</p>