The critical exponent(s) for the semilinear fractional diffusive equation
Analysis of PDEs
2018-07-02 v1
Abstract
In this paper we show that there exist two different critical exponents for global small data solutions to the semilinear fractional diffusive equation with Caputo fractional derivative in time. The second critical exponent appears if the second data is assumed to be zero. This peculiarity is related to the fact that the order of the equation is fractional. To prove our result, we first derive Lr-Lq linear estimates for the solution to the inhomogeneous linear Cauchy problem and then we apply a contraction argument.
Keywords
Cite
@article{arxiv.1709.03285,
title = {The critical exponent(s) for the semilinear fractional diffusive equation},
author = {Marcello D'Abbicco and Marcelo Rempel Ebert and Tiago Henrique Picon},
journal= {arXiv preprint arXiv:1709.03285},
year = {2018}
}