L1 contraction for bounded (nonintegrable) solutions of degenerate parabolic equations
Journal article, Peer reviewed
Date
2014-12-11Metadata
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- Institutt for matematiske fag [2341]
- Publikasjoner fra CRIStin - NTNU [36890]
Abstract
We obtain new L1 contraction results for bounded entropy solutions of Cauchy
problems for degenerate parabolic equations. The equations we consider have possibly strongly
degenerate local or nonlocal diffusion terms. As opposed to previous results, our results apply without
any integrability assumption on the solutions. They take the form of partial Duhamel formulas and
can be seen as quantitative extensions of finite speed of propagation local L1 contraction results
for scalar conservation laws. A key ingredient in the proofs is a new and nontrivial construction of
a subsolution of a fully nonlinear (dual) equation. Consequences of our results are maximum and
comparison principles, new a priori estimates, and, in the nonlocal case, new existence and uniqueness
results.