| Autor: |
ENDAL, J., JAKOBSEN, E. R. |
| Předmět: |
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| Zdroj: |
SIAM Journal on Mathematical Analysis; 2014, Vol. 46 Issue 6, p3957-3982, 26p |
| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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