A Livšic Theorem for Matrix Cocycles Over Non-uniformly Hyperbolic Systems
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DOI: 10.1007/s10884-018-9691-x
Abstract: We prove a Livšic-type theorem for Hölder continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever $$(f,\mu )$$(f,μ) is a non-uniformly hyperbolic system and $$A:M \rightarrow GL(d,\mathbb {R}) $$A:M→GL(d,R) is… read more here.
Keywords: hyperbolic systems; matrix; uniformly hyperbolic; lder continuous ... See more keywords
Explicit solution for a class of coupled hyperbolic systems of conservation laws
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DOI: 10.1080/00036811.2019.1612883
Abstract: ABSTRACT Under suitably generalized Rankine–Hugoniot relation and entropy condition, by introducing a convex hull of potential function, the global explicit solution for the Cauchy problem to a class of coupled hyperbolic systems of conservation laws,… read more here.
Keywords: explicit solution; hyperbolic systems; class coupled; systems conservation ... See more keywords
Representations of the solutions of the first-order elliptic and hyperbolic systems via harmonic and wave functions respectively
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DOI: 10.1080/17476933.2019.1669570
Abstract: ABSTRACT In this paper representations of the solutions of all first-order elliptic and hyperbolic systems in three-dimensional and four-dimensional spaces are obtained through the derivatives of harmonic and wave functions, respectively. read more here.
Keywords: representations solutions; hyperbolic systems; first order; order elliptic ... See more keywords
Unstable entropies and dimension theory of partially hyperbolic systems
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DOI: 10.1088/1361-6544/ac3dcb
Abstract: In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory–Pesin dimension characteristic, motivated by the work of Bowen and Pesin etc. We… read more here.
Keywords: partially hyperbolic; unstable topological; dimension theory; hyperbolic systems ... See more keywords
Fast Convergence Methods for Hyperbolic Systems of Balance Laws with Riemann Conditions
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DOI: 10.3390/sym12050757
Abstract: In this paper, we develop an accurate technique via the use of the Adomian decomposition method (ADM) to solve analytically a 2 × 2 systems of partial differential equation that represent balance laws of hyperbolic-elliptic… read more here.
Keywords: methods hyperbolic; hyperbolic systems; fast convergence; balance laws ... See more keywords