Regularization for fractional integral. Application to nonlinear equations with singularities
Year: 2003
Type: preprint
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 Schrödinger 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 $t.$ We do the same for linear Schrödinger equation.
Source: arXiv (Cornell University)
Author: Stojanovic, Mirjana
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1647035120