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

TL;DR

This paper introduces a new non-degeneracy condition ensuring strong precompactness of bounded sequences under nonlinear constraints, and applies it to prove decay properties of periodic entropy solutions in multidimensional scalar conservation laws.

Contribution

It presents a novel non-degeneracy condition that guarantees strong precompactness and demonstrates its application to decay of periodic entropy solutions.

Findings

Established a new non-degeneracy condition for precompactness.

Proved decay of periodic entropy solutions in multidimensional cases.

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.