Blow-up for a non-linear stable non-Gaussian process in fractional time
Probability
2022-12-21 v3 Functional Analysis
Abstract
The behaviour of solutions for a non-linear diffusion problem is studied. A subordination principle is applied to obtain the variation of parameters formula in the sense of Volterra equations, which leads to the integral representation of a solution in terms of the fundamental solutions. This representation, the so-called mild solution, is used to investigate some properties about continuity and non-negativeness of solutions as well as to prove a Fujita type blow-up result. Fujita's critical exponent is established in terms of the parameters of the stable non-Gaussian process and a result for global solutions is given.
Keywords
Cite
@article{arxiv.2109.05305,
title = {Blow-up for a non-linear stable non-Gaussian process in fractional time},
author = {S. Solís and V. Vergara},
journal= {arXiv preprint arXiv:2109.05305},
year = {2022}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:2105.01272