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T5 configurations and hyperbolic systems.
- Source :
-
Communications in Contemporary Mathematics . Apr2024, Vol. 26 Issue 3, p1-21. 21p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Müller and V. Šverák, Studying Nonlinear PDE by Geometry in Matrix Space (Springer, 2003), Sec. 7], and many of its properties have already been shown in [A. Lorent and G. Peng, Null Lagrangian measures in subspaces, compensated compactness and conservation laws, Arch. Ration. Mech. Anal. 234(2) (2019) 857–910; A. Lorent and G. Peng, On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity, Calc. Var. Partial Differential Equations 59(5) (2020) 156]. In particular, in [A. Lorent and G. Peng, On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity, Calc. Var. Partial Differential Equations 59(5) (2020) 156], it is shown that the differential inclusion does not contain any T 4 configurations. Here, we continue that study by showing that the differential inclusion does not contain T 5 configurations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 26
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176107737
- Full Text :
- https://doi.org/10.1142/S021919972250081X