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November/December 2017 Existence of solutions to a class of weakly coercive diffusion equations with singular initial data
Marco Papi, Maria Michaela Porzio, Flavia Smarrazzo
Adv. Differential Equations 22(11/12): 893-962 (November/December 2017).

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

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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.

Information

Published: November/December 2017
First available in Project Euclid: 1 September 2017

zbMATH: 1377.35167
MathSciNet: MR3692914

Subjects:
Primary: 28A33, 35K20, 35K65

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.22 • No. 11/12 • November/December 2017
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