Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Abstract
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
Cite
@article{arxiv.1003.0048,
title = {Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study},
author = {Luiz Carlos Lobato Botelho},
journal= {arXiv preprint arXiv:1003.0048},
year = {2019}
}
Comments
In order to protest against that stupid and ruthless decision of arxiv moderation in not allow me to submit unplished articles in arxiv 20 pages