singular limit for relaxation and viscosity approximations of extended traffic flow models.
stability of conservation laws for a traffic flow model.
-type contraction for systems of conservation laws
The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in . However it is not a contraction in for any . Leger showed in [20] that for a convex flux, it is however a contraction in up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...
-decay of solutions to dissipative-dispersive perturbations of conservation laws
We study the decay in time of the spatial -norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.
Large Time Behavior of Solutions of Hyperbolic Balance laws
Large time behaviour of a class of solutions of second order conservation laws
% We study the large time behaviour of entropy solutions of the Cauchy problem for a possibly degenerate nonlinear diffusion equation with a nonlinear convection term. The initial function is assumed to have bounded total variation. We prove the convergence of the solution to the entropy solution of a Riemann problem for the corresponding first order conservation law.
Large time behaviour of a diffusion equation with strong convection
Leggi di conservazione
Limite de la solution de ut - ∆um + div F(u) = 0 lorsque m --> ∞.
Dans cette article, on étudie la limite lorsque m --> ∞ de la solution du problème de Cauchy ut - ∆um + div F(u) = 0 sur un ouvert Omega avec des conditions aux bords de type Dirichlet et une donnée initiale u0 ≥ 0.
Linear degeneracy and shock waves.
Line-energy Ginzburg-Landau models : zero-energy states
We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful...
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method...
Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity