Nonlinear parabolic equations with singularities in colombeau vector spaces

Abstract

We consider nonlinear parabolic equations with nonlinear non-Lipschitz's term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space G C 1,W 2,2 ([0,T),R n ),n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space G C 1, L 2 ([0,T),R n ),n ≤ 3. © Springer-Verlag 2006.