Abstract
We consider several types of nonlinear parabolic equations with singular \(\delta\) like potential and initial data. To prove the existence-uniqueness theorems we employ regularized derivatives. As a framework we use Colombeau space \({\cal G}_{p,q}\) \(([0,T)\) \(\times \bf{R}^n),\) \(1 \leq p,q \leq \infty,\) and Colombeau vector space \({\cal G}_{C^1,L^2}([0,T), \bf{R}^n).\)
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Stojanović, M. Nonlinear Parabolic Equations with Regularized Derivatives in Colombeau Algebra. Acta Appl Math 92, 1–14 (2006). https://doi.org/10.1007/s10440-006-9036-3
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DOI: https://doi.org/10.1007/s10440-006-9036-3