Heat equation with singular potential and singular data

Authors: Nedeljkov, M.; Pilipovi cacute , S.; Rajter- Cacute iri cacute , D.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 135, Number 4, August 2005 , pp. 863-886(24)

Publisher: Royal Society of Edinburgh

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Abstract:

Nets of Schrödinger C₀-semigroups (S) with the polynomial growth with respect to are used for solving the Cauchy problem (_t - Delta

)U + VU = f(t, U), U(0, x) = U₀(x) in a suitable generalized function algebra (or space), where V and U₀ are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

Document Type: Research article

Publication date: 2005-08-01