On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws

Evgeny Yu.  Panov; Evgeny Yu.  Panov

doi:10.3934/nhm.2016.11.349

Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 349-367. doi: 10.3934/nhm.2016.11.349

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On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws

Evgeny Yu. Panov ^{1
,}

1.
Novgorod State University, 41 B. Sankt-Peterburgskaya, 173003 Veliky Novgorod

Received: 01 April 2015 Revised: 01 June 2015
Primary: 35L65, 35B10; Secondary: 35B40.

We propose a new sufficient non-degeneracy condition for the strong precompactness of bounded sequences satisfying the nonlinear first-order differential constraints. This result is applied to establish the decay property for periodic entropy solutions to multidimensional scalar conservation laws.
- H-measures,
- localization principles,
- conservation laws,
- periodic entropy solutions,
- decay property
Citation: Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws[J]. Networks and Heterogeneous Media, 2016, 11(2): 349-367. doi: 10.3934/nhm.2016.11.349

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Abstract

We propose a new sufficient non-degeneracy condition for the strong precompactness of bounded sequences satisfying the nonlinear first-order differential constraints. This result is applied to establish the decay property for periodic entropy solutions to multidimensional scalar conservation laws.

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