Regularization for fractional integral. Application to nonlinear equations with singularities
Analysis of PDEs
2007-05-23 v1 Functional Analysis
Abstract
We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar kernel and nonlinear parabolic equations (of ordinary type, with nonlinear conservative term and with Schr\"odinger kernel) with strongly singular initial data and non-Lipschitz nonlinearities. In a case of nonlinear parabolic equations we do in fact regularization of heat semigroup with delta sequence with respect to the time variable We do the same for linear Schr\"odinger equation.
Cite
@article{arxiv.math/0311464,
title = {Regularization for fractional integral. Application to nonlinear equations with singularities},
author = {Mirjana Stojanovic},
journal= {arXiv preprint arXiv:math/0311464},
year = {2007}
}