相关论文: Hyperbolic Balance Laws with a Non Local Source

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…

We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…

In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…

This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…

We consider the $2 \times 2$ parabolic systems \begin{equation*} u^{\epsilon}_t + A(u^{\epsilon}) u^{\epsilon}_x = \epsilon u^{\epsilon}_{xx} \end{equation*} on a domain $(t, x) \in ]0, + \infty[ \times ]0, l[$ with Dirichlet boundary…

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This…

We write a first order symmetric hyperbolic system coupling the Riemann with the dynamical acceleration of a relativistic fluid. W determine the associated, coupled, Bel - Robinson energy, and the integral equality that it satisfies.

The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…

This paper investigates the regularity of Lipschitz solutions $u$ to the general two-dimensional equation $\text{div}(G(Du))=0$ with highly degenerate ellipticity. Just assuming strict monotonicity of the field $G$ and heavily relying on…

We consider the dependence of the entropic solution of a hyperbolic system of conservation laws \[ \{\{array}{c} u_t + f(u)_x = 0 u(0,\cdot) = u_0 \{array} \] on the flux function f. We prove that the solution in Lipschitz continuous…

This paper proves the local-in-time strong well-posedness of a parabolic-hyperbolic regularized version of Hibler's sea ice model. Hibler's model is the most frequently used sea ice model in climate science. Lagrangian coordinates are…

In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton's principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an…

We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth order in space and describe the behavior of the main components…

Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are…

We give examples of quasi-hyperbolic dynamical systems with the following properties : polynomial decay of correlations, convergence in law toward a non gaussian law of the ergodic sums (divided by $n^{3/4}$) associated to non degenerated…

The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…

This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…

We are concerned with quasilinear symmetrizable partially dissipative hyperbolic systems in the whole space $\mathbb{R}^d$ with $d\geq2$. Following our recent work [10] dedicated to the one-dimensional case, we establish the existence of…

We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear…

We consider the Schr\"odinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we get strong well-posedness…