Abstract
We prove existence of suitably defined 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 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.
Citation
Marco Papi. Maria Michaela Porzio. Flavia Smarrazzo. "Existence of solutions to a class of weakly coercive diffusion equations with singular initial data." Adv. Differential Equations 22 (11/12) 893 - 962, November/December 2017. https://doi.org/10.57262/ade/1504231226
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