We investigate the spectral types of families of discrete one-dimensional Schrödinger operators $\{H_\omega\}_{\omega\in\Omega}$, where each $H_\omega$ has a potential function $V_\omega(n)=f(T^n\omega)$ for $n\in\mathbb{Z}$, $T$ is an ergodic …
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying significant type of …
In this paper, we study the Riemann problem for a general variable coefficient Burgers equation with time-dependent damping. We use a nonlinear time-dependent viscosity equation with a similarity variable. Thus, when the viscosity goes to zero, we …
A través de estas notas de clase, se pretende que el aprendizaje sea accesible a la comunidad académica en especial a los estudiantes y profesores con una buena formación matemática, con esta obra de bajo costo. Los temas tratados aquí son una …
In this paper, we study two systems with a time-variable coefficient and general time-gradually-degenerate damping. More explicitly, we construct the Riemann solutions to the time-variable coefficient Zeldovich approximation and time-variable …
A homoclinic class is the closure of the transverse intersection points of the stable and unstable manifolds of a hyperbolic periodic orbit. In this paper, we prove, using the techniques presented in [1], that the Plykin and the Solenoid attractors …
We consider a class of endomorphisms that contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. Our goal is to study a class of endomorphisms that preserve a foliation that is almost everywhere …
In this paper, we apply the method given in the paper “Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors” (Mathematische Annalen, 2022, 382: 1031–1046) to study the Cauchy problem for a one dimensional …
In this paper we study a new property for the Glimm potential introduced by L. Caravenna [3]. This new property enable us to study scalar conservation laws with a particular source term called linear damping. By the operator splitting method joined …
We consider a robust class of random non-uniformly expanding local homeomorphisms and Hölder continuous potentials with small variation. For each element of this class we develop the thermodynamical formalism and prove the existence and uniqueness of …