Analysis & PDE
- Anal. PDE
- Volume 6, Number 7 (2013), 1719-1754.
Pseudoparabolic regularization of forward-backward parabolic equations: A logarithmic nonlinearity
We study the initial-boundary value problem
with measure-valued initial data, assuming that the regularizing term has logarithmic growth (the case of power-type was dealt with in an earlier work). We prove that this case is intermediate between the case of power-type and that of bounded , to be addressed in a forthcoming paper. Specifically, the support of the singular part of the solution with respect to the Lebesgue measure remains constant in time (as in the case of power-type ), although the singular part itself need not be constant (as in the case of bounded , where the support of the singular part can also increase). However, it turns out that the concentrated part of the solution with respect to the Newtonian capacity remains constant.
Anal. PDE, Volume 6, Number 7 (2013), 1719-1754.
Received: 18 July 2012
Revised: 12 November 2012
Accepted: 20 December 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35D99: None of the above, but in this section 35K55: Nonlinear parabolic equations 35R25: Improperly posed problems
Secondary: 28A33: Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 28A50: Integration and disintegration of measures
Bertsch, Michiel; Smarrazzo, Flavia; Tesei, Alberto. Pseudoparabolic regularization of forward-backward parabolic equations: A logarithmic nonlinearity. Anal. PDE 6 (2013), no. 7, 1719--1754. doi:10.2140/apde.2013.6.1719. https://projecteuclid.org/euclid.apde/1513731434