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Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
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Michiel Bertsch
,
Flavia Smarrazzo
Published/Copyright:
January 28, 2014
Abstract
We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type. We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.
Received: 2012-5-3
Revised: 2013-11-9
Published Online: 2014-1-28
Published in Print: 2016-3-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
