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Regularization for fractional integral. Application to nonlinear equations with singularities

Research paper by Mirjana Stojanovic

Indexed on: 26 Nov '03Published on: 26 Nov '03Published in: Mathematics - Analysis of PDEs



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 $t.$ We do the same for linear Schr\"odinger equation.