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
...... 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
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-measu...... 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
One dimensional lattice gases with rapidly decreasing interactionArchive for Rational Mechanics and Analysis - Tập 37 - Trang 181-191 - 1970
G. Gallavotti, T. F. Lin
We consider the pressure and the correlation functions of a one dimensional lattice gas in which the mutual interaction decreases as r exp-n
t, (r, t>0), when the interparticle distance n→∞. We prove that such a system cannot show phase transitions of order k≧1 in the sense that the pressure and the correlation functions are infinitely differentiable with respect to any relevant parameter (such as...... hiện toàn bộ