Stojanovi., Mirjana, Nonlinear Parabolic Equations with Singularities in Colombeau Vector Spaces, Acta mathematica Sinica. English series (Print) , 22(2), 2006, pp. 393-406
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 GC1,W2,2([0,T),Rn,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 GC1,L2([0,T),Rn,n.3.