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

#### 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.
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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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