arXiv subjects

J. M. Mazón

Publications and source records attributed to J. M. Mazón.

3 recordsLinked to original sources

arXiv2026

Doubly Nonlinear Diffusion Equations on Metric Graphs

In this paper we study existence and uniqueness of solutions for a very general class of doubly nonlinear diffusion equations on metric graphs, which provide the appropriate mathematical framework to describe complex tubular networks in which axial diffusion is the main focus. Some important particular cases covered in our study are the Porous Medium Equation and the evolution equation for the $p$-Laplacian, but we also consider the case in that diffusion changes from one edge to another, which takes into account the influence of the properties of the tubules forming the network on axial diffusion. Furthermore, the problem is studied under non-homogeneous Neumann-Kirchhoff conditions on the vertices of the graph.

math.AP↗

arXiv2025

Evolution problem for the $1$-Laplacian with mixed boundary conditions

This paper deals with evolution problem for the $1$-Laplacian with mixed boundary conditions on a bounded open set $Ω$ of $\R^N$. We prove existence and uniqueness of strong solutions for data in $L^2(Ω)$ by mean of the theory of maximal monotone operator. We also see that if the flux on the boundary is~$1$ (that is, the maximum possible) then these strong solutions can be seen as the large solutions introduced in \cite{MP}. We give explicit examples of solutions.

math.AP↗

arXiv2025

Evolution problems with perturbed $1$-Laplacian type operators on random walk spaces

Random walk spaces are a general framework for the study of PDEs. They include as particular cases locally finite weighted connected graphs and nonlocal settings involving symmetric integrable kernels on $\mathbb{R}^N$. We are interested in the study of evolution problems involving two random walk structures so that the associated functionals have different growth on each structure. We also deal with the case of a functional with different growth on a partition of the random walk.

math.AP↗