Related papers: One Dimensional Hyperbolic Conservation Laws: Past…
We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…
This article summarizes the proposal to address the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED). The proposed mechanism is described, emphasizing the relaxation mechanism which ensures…
In this article, we consider scalar conservation laws with fluxes having spatial discontinuities and possible flat regions and study the following three aspects: (i) existence, (ii) uniqueness and (iii) BV regularity of solutions. We…
We illustrate and emphasize the relevance of hyperbolic theories of dissipation in different physical scenarios. Particular attention is paid to self-gravitating systems where the relaxation time may become large enough as to require a…
We review the conservation laws of magnetohydrodynamics (MHD) in an expanding homogeneous and isotropic Universe that can be applied to the study of early Universe physics during the epoch of radiation domination. The conservation laws for…
We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial…
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
The one-dimensional toy models proposed for the three-dimensional electron magnetohydrodynamics in our previous work share some similarities with the original dynamics under certain symmetry. We continue to study the well-posedness issue…
In this paper we study the problem of the global existence (in time) of weak, entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase…
An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is…
We provide global and semi-global controllability results for hyperbolic conservation laws on a bounded domain, with a general (not necessarily convex)flux and a time-dependent source term acting as a control. The results are achieved for,…
We prove existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Holder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction,…
Nonlinear scalar conservation laws are traditionally viewed as transport equations. We take instead the viewpoint of these PDEs as continuity equations with an implicitly defined velocity field. We show that a weak solution is the entropy…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
These notes describe some applications of the analysis of ordinary differential equations to the study of the viscous approximation of conservation laws in one space dimension. The exposition mostly focuses on the analysis of invariant…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
We study the effects of strict conservation laws and the problem of negative contributions to final momentum distribution during the freeze out through 3-dimensional hypersurfaces with space-like normal. We study some suggested solutions…
We propose some one-dimensional reduced models for the three-dimensional electron magnetohydrodynamics which involves a highly nonlinear Hall term with intricate structure. The models contain nonlocal nonlinear terms. Local well-posedness…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…