Advances in Differential Equations

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

Marco Papi, Maria Michaela Porzio, and Flavia Smarrazzo

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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.

Article information

Source
Adv. Differential Equations Volume 22, Number 11/12 (2017), 893-962.

Dates
First available in Project Euclid: 1 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1504231226

Zentralblatt MATH identifier
1377.35167

Subjects
Primary: 35K20: Initial-boundary value problems for second-order parabolic equations 28A33: Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 35K65: Degenerate parabolic equations

Citation

Papi, Marco; Porzio, Maria Michaela; Smarrazzo, Flavia. Existence of solutions to a class of weakly coercive diffusion equations with singular initial data. Adv. Differential Equations 22 (2017), no. 11/12, 893--962. https://projecteuclid.org/euclid.ade/1504231226


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