Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study

Details Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study

2010-02-27

arxiv.org/abs/1003.0048v1

Physics

General Physics

20 pages

Scientific paper

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.

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