We prove existence of suitably defined {\em measure-valued solutions} to the homogeneous Dirichlet initial-boundary value problem with a Radon measure as initial datum, for a class of degenerate parabolic equations without strong coerciveness. The notion of solution is natural, since it is obtained by a suitable {\em approximation procedure} which can be regarded as a first step towards a continuous dependence on the initial data. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part.

Existence of solutions to a class of weakly coercive diffusion equations with singular initial data / Papi, Marco; Porzio, Maria Michaela; Smarrazzo, Flavia. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 22:11-12(2017), pp. 893-962.

Existence of solutions to a class of weakly coercive diffusion equations with singular initial data

PORZIO, Maria Michaela;
2017

Abstract

We prove existence of suitably defined {\em measure-valued solutions} to the homogeneous Dirichlet initial-boundary value problem with a Radon measure as initial datum, for a class of degenerate parabolic equations without strong coerciveness. The notion of solution is natural, since it is obtained by a suitable {\em approximation procedure} which can be regarded as a first step towards a continuous dependence on the initial data. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part.
Evolution problems, existence of solutions, weakly coercive diffusion equations, singular initial data
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Existence of solutions to a class of weakly coercive diffusion equations with singular initial data / Papi, Marco; Porzio, Maria Michaela; Smarrazzo, Flavia. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 22:11-12(2017), pp. 893-962.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/951679
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