Related papers: Generic Structural Stability for $2 \times 2$ Syst…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
We study the regularity of sonic curves to a two-dimensional Riemann problem for the nonlinear wave system of Chaplygin gas, which is an essential step for the global existence of solutions to the two-dimensional Riemann problems. As a…
We consider a system consisting of one conservation law and one balance law with a time-dependent source term, and provide a comprehensive analysis of Riemann solutions, including the non-classical overcompressive delta shocks. The minimal…
Zeitlin's model is a discretisation of the 2-D Euler equations that preserves the underlying geometric structure. This feature makes it suitable for studying the qualitative behaviour of the dynamics. Here, we utilise Arnold's geometric…
We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification…
In this paper, we show that a geometrical condition on $2\times2$ systems of conservation laws leads to non-uniqueness in the class of 1D continuous functions. This demonstrates that the Liu Entropy Condition alone is insufficient to…
We obtain a generic regularity result for stationary integral $n$-varifolds with only strongly isolated singularities inside $N$-dimensional Riemannian manifolds, in absence of any restriction on the dimension ($n\geq 2$) and codimension.…
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…
In this article, we investigate the BV stability of $2\times 2$ hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing…
In this paper we study the global exponential stability in the $L^{2}$ norm of semilinear $1$-$d$ hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient…
We propose an extended structural dynamics framework that enriches classical mechanics by treating particle orientation and internal structure as fundamental phase-space coordinates. This extension preserves Hamiltonian structure and…
In this paper, we prove the uniform nonlinear structural stability of Hagen-Poiseuille flows with arbitrary large fluxes in the axisymmetric case. This uniform nonlinear structural stability is the first step to study Liouville type theorem…
In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The…
We give sufficient conditions for Input-to-State Stability in $C^{1}$ norm of general quasilinear hyperbolic systems with boundary input disturbances. In particular the derivation of explicit Input-to-State Stability conditions is discussed…
We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Ito) noise. The Cauchy problem defined on a Riemannian manifold is shown to be well-posed. We prove existence of generalized kinetic…
The stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability of a non-linear scheme in terms of its cor- responding scheme in…
A topological argument is presented for nodal structures of superconducting states with time-reversal invariance. A generic Hamiltonian which describes a quasiparticle in superconducting states with time-reversal invariance is derived, and…
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of…
About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed…
In this paper, we provide a new criterion for the stable transitivity of volume preserving finite generated group on any compact Riemannian manifold. As one of our applications, we generalised a result of Dolgopyat and Krikorian in…