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- Title
Semi-linear diffusion in and in Hilbert spaces, a Feynman-Wiener path integral study.
- Authors
Botelho, Luiz C. L.
- 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 useful for modeling 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 rigorous functional integral solutions for the linear diffusion and wave equations 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.
- Subjects
NONLINEAR theories; HILBERT space; PATH integrals; EXISTENCE theorems; PROOF theory; DIMENSIONAL analysis; WHITE noise theory; WAVE equation
- Publication
Random Operators & Stochastic Equations, 2011, Vol 19, Issue 4, p361
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/ROSE.2011.020