Multiple Brake Orbits and Homoclinics in Riemannian ManifoldsArchive for Rational Mechanics and Analysis - Tập 200 - Trang 691-724 - 2010
Roberto Giambò, Fabio Giannoni, Paolo Piccione
Let (M, g) be a complete Riemannian manifold, $${\Omega\subset M}$$ an open
subset whose closure is homeomorphic to an annulus. We prove that if ∂Ω is
smooth and it satisfies a strong concavity assumption, then there are at least
two distinct geodesics in $${\overline\Omega=\Omega\cup\partial\Omega}$$
starting orthogonally to one connected component of ∂Ω and arriving orthogonally
onto the other o... hiện toàn bộ
On Entropy Solutions of Scalar Conservation Laws with Discontinuous FluxArchive for Rational Mechanics and Analysis - Tập 247 - Trang 1-40 - 2023
Evgeny Yu. Panov
We introduce the notion of entropy solutions (e.s.) to a conservation law with
an arbitrary jump continuous flux vector and prove the existence of the largest
and the smallest e.s. to the Cauchy problem. The monotonicity and stability
properties of these solutions are also established. In the case of a periodic
initial function, we derive the uniqueness of e.s. Generally, the uniqueness
property c... hiện toàn bộ
Kinetic Relations for a Lattice Model of Phase TransitionsArchive for Rational Mechanics and Analysis - Tập 206 - Trang 707-724 - 2012
Hartmut Schwetlick, Johannes Zimmer
The aim of this article is to analyse travelling waves for a lattice model of
phase transitions, specifically the Fermi–Pasta–Ulam chain with piecewise
quadratic interaction potential. First, for fixed, sufficiently large subsonic
wave speeds, we rigorously prove the existence of a family of travelling wave
solutions. Second, it is shown that this family of solutions gives rise to a
kinetic relati... hiện toàn bộ
Directional Oscillations, Concentrations, and Compensated Compactness via Microlocal Compactness FormsArchive for Rational Mechanics and Analysis - Tập 215 - Trang 1-63 - 2014
Filip Rindler
This work introduces microlocal compactness forms (MCFs) as a new tool to study
oscillations and concentrations in L p -bounded sequences of functions.
Decisively, MCFs retain information about the location, value distribution, and
direction of oscillations and concentrations, thus extending at the same time
the theories of (generalized) Young measures and H-measures. In L p -spaces
oscillations a... hiện toàn bộ
On the Structure of $${L^\infty}$$ -Entropy Solutions to Scalar Conservation Laws in One-Space DimensionArchive for Rational Mechanics and Analysis - Tập 226 - Trang 441-493 - 2017
S. Bianchini, E. Marconi
We prove that if u is the entropy solution to a scalar conservation law in one
space dimension, then the entropy dissipation is a measure concentrated on
countably many Lipschitz curves. This result is a consequence of a detailed
analysis of the structure of the characteristics. In particular, the
characteristic curves are segments outside a countably 1-rectifiable set and the
left and right trace... hiện toàn bộ