Advances in Differential Equations
- Adv. Differential Equations
- Volume 22, Number 11/12 (2017), 893-962.
Existence of solutions to a class of weakly coercive diffusion equations with singular initial data
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.
Adv. Differential Equations, Volume 22, Number 11/12 (2017), 893-962.
First available in Project Euclid: 1 September 2017
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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